<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/><b>let </b><font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:70"/><i><font color="Green">E45</font></i>: 
not <font color="Maroon">R</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon">p</font> be  <a href="ami_1.html#V11">autonomic</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:70"/><i><font color="Green">E57</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E3:70"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font>
 <b>and </b><br/><a NAME="E4:70"/><i><font color="Green">E62</font></i>: 
 <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font>
 <b>and </b><br/><a NAME="E5:70"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/>

<a NAME="E6:70"/><i><font color="Green">E74</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:70"><i><font color="Green">E45</font></i></a></i>;<br/>
<a NAME="E7:70"/><i><font color="Green">E76</font></i>: 
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K7">DataPart</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2"><i><font color="Green">Lemma41</font></i></a></i>;<br/>
<a NAME="E8:70"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/>
<a NAME="E9:70"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E10:70"/>
 <a href="ami_5.html#K7">DataPart</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/>
<a NAME="E11:70"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="ami_5.html#K7">DataPart</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E12:70"/><i><font color="Green">E79</font></i>: 
not <font color="Maroon">p</font> is <a href="ami_3.html#V1">programmed</a>
 
<b>by </b><i>, <a class="ref" href="ami_5.html#T76">AMI_5:76</a></i>;<br/>
<a NAME="E13:70"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 
<b>by </b><i>, <a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmring4.html#E12"><i><font color="Green">Lemma58</font></i></a>, </i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> &amp;  <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  );<br/>
<a NAME="E14:70"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>
<br/>.= 
 <a href="ami_3.html#K13">IC</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmring4.html#E13"><i><font color="Green">Lemma59</font></i></a>, <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/>

<a NAME="E2:70_1"/><i><font color="Green">E82</font></i>: 
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font>
 
<b>by </b><i>, , <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>;<br/>
<a NAME="E3:70_1"/><b>then </b>
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<a NAME="E4:70_1"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, </i>;<br/>
<a NAME="E5:70_1"/>
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T63">AMI_5:63</a></i>;<br/>
<a NAME="E6:70_1"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E7:70_1"/><b>then </b>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K5">pi</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">I</font> = <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> ;<br/>
<a NAME="E9:70_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmring4.html#T10" target="_self">Th10</a>, <a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<i><font color="Green">E113</font></i>:  <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span></span>)</span>,<font color="Maroon">k</font> = 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">s1</font></span>)</span>,<font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span>,<font color="Maroon">k</font>

;<br/>
<a NAME="E11:70_1"/><i><font color="Green">E114</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:70"><i><font color="Green">E45</font></i></a></i>;<br/>
<a NAME="E12:70_1"/><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T1" target="_self">Th1</a></i>;<br/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">s2</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<b>hence </b><a NAME="E14:70_1"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="txt" href="scmring4.html#E5:70"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmring4.html#T5" target="_self">Th5</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> = 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font>
<b>by </b><i><a class="txt" href="scmring4.html#E3:70"><i><font color="Green">E61</font></i></a>, <a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T8" target="_self">Th8</a>, <a class="txt" href="scmring4.html#E4:70"><i><font color="Green">E62</font></i></a>, <a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T8" target="_self">Th8</a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/>

<a NAME="E16:70_1"/><i><font color="Green">E116</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="txt" href="scmring4.html#E12"><i><font color="Green">Lemma58</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i>, <a class="ref" href="funct_4.html#T24">FUNCT_4:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E15:70"/><i><font color="Green">E117</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:70_2"/><i><font color="Green">E118</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E2:70_2"/><i><font color="Green">E119</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E3:70_2"/><i><font color="Green">E120</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:70_2"/><i><font color="Green">E121</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>set </b><font color="Maroon">Cs1i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">Cs2i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">Cs3i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">Cs1i1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">Cs2i1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">Cs3i1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">DPp</font> =  <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font>;<br/>
<a NAME="E5:70_2"/><i><font color="Green">E122</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</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="ami_5.html#K7">DataPart</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2"><i><font color="Green">Lemma41</font></i></a></i>;<br/>
<a NAME="E6:70_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E7:70_2"/><b>then </b><i><font color="Green">E123</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E8:70_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E9:70_2"/><b>then </b><i><font color="Green">E124</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E10:70_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E11:70_2"/><b>then </b><i><font color="Green">E125</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E12:70_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E13:70_2"/><b>then </b><i><font color="Green">E126</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E14:70_2"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E15:70_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<a NAME="E16:70_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E17:70_2"/><b>then </b><i><font color="Green">E127</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/>
<a NAME="E18:70_2"/><b>then </b><i><font color="Green">E129</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/>
<a NAME="E19:70_2"/><i><font color="Green">E130</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="txt" href="scmring4.html#E7:70"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/>
<i><font color="Green">E131</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E9:70"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<i><font color="Green">E132</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p4">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E11:70"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E22:70_2"/><i><font color="Green">E133</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E6:70"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmring4.html#E7:70"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/>
<a NAME="E23:70_2"/><i><font color="Green">E134</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="scmring4.html#E7:70"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/>
<i><font color="Green">E135</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E14:70"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<i><font color="Green">E136</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p4">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E26:70_2"/><i><font color="Green">E137</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E27:70_2"/><i><font color="Green">E138</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E28:70_2"/><i><font color="Green">E139</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E29:70_2"/><i><font color="Green">E140</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E30:70_2"/><i><font color="Green">E141</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmring4.html#E2"><i><font color="Green">Lemma41</font></i></a></i>;<br/>
<a NAME="E31:70_2"/><i><font color="Green">E142</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E143</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><a NAME="E1:70_2_5"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><b>hence </b><a NAME="E2:70_2_5"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E144</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><a NAME="E1:70_2_6"/><i><font color="Green">E145</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="scmring4.html#T16" target="_self">Th16</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="txt" href="scmring4.html#E5:70"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E146</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:70_2_7"/><i><font color="Green">E147</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:70_2_7"/><i><font color="Green">E148</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 ;<br/><a NAME="E3:70_2_7"/><i><font color="Green">E149</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, , , <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, <a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, <a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E150</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:70_2_8"/><i><font color="Green">E151</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:70_2_8"/><i><font color="Green">E159</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, <a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E160</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_9"/><i><font color="Green">E161</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 ;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E162</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_10"/><i><font color="Green">E202</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 ;<br/><a NAME="E2:70_2_10"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/><b>hence </b><a NAME="E3:70_2_10"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E5:70"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, <a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E203</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_11"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_2_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_11"/><b>then </b><i><font color="Green">E204</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
 ;<br/><b>reconsider </b><font color="Maroon">loc</font> =  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> ;<br/><a NAME="E4:70_2_11"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">loc</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, </i>;<br/><a NAME="E5:70_2_11"/>
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T63">AMI_5:63</a></i>;<br/><a NAME="E6:70_2_11"/><b>then </b><i><font color="Green">E206</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><i><font color="Green">E207</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<font color="Maroon">s1</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">loc</font>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">loc</font>
<b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><a NAME="E8:70_2_11"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">loc</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K5">pi</a> <font color="Maroon">p</font>,<font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">I</font> = <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">loc</font> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> ;<br/><a NAME="E10:70_2_11"/>
<font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T1" target="_self">Th1</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span> = 
<font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E2:70"><i><font color="Green">E57</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
;<br/><b>hence </b><a NAME="E12:70_2_11"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T30" target="_self">Th30</a>, <a class="ref" href="scmring4.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div>
<i><font color="Green">E208</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>

;<br/>
<i><font color="Green">E209</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>

;<br/>
<i><font color="Green">E210</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , </i>
;<br/>
<b>consider </b><font color="Maroon">j</font> being  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E43:70_2"/><i><font color="Green">E211</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T26">AMISTD_1:26</a></i>;<br/>
<i><font color="Green">E212</font></i>:  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T30" target="_self">Th30</a>, </i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T67">SCMRING3:67</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring2.html#K11">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="scmring4.html#T30" target="_self">Th30</a>, <a class="ref" href="scmring3.html#T67">SCMRING3:67</a></i>
;<br/>
<b>set </b><font color="Maroon">I</font> =  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>;<br/>
<a NAME="E45:70_2"/><i><font color="Green">E213</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 7
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 7 )
 </span><b>by </b><i><a class="ref" href="scmring4.html#T32" target="_self">Th32</a>, <a class="ref" href="cqc_the1.html#T8">CQC_THE1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_1"><b>suppose </b></a><a NAME="E1:70_2_16_1"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:70_2_16_1"/><b>then </b><i><font color="Green">E214</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16">SCMRING3:16</a></i>;<br/><a NAME="E3:70_2_16_1"/><b>then </b><i><font color="Green">E215</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/><b>hence </b><a NAME="E5:70_2_16_1"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E6:70_2_16_1"/><i><font color="Green">E216</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/><b>hence </b><a NAME="E7:70_2_16_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E8:70_2_16_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmring4.html#E5:70"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2"><b>suppose </b></a><a NAME="E1:70_2_16_2"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:70_2_16_2"/><i><font color="Green">E217</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T17">SCMRING3:17</a></i>;<br/><a NAME="E4:70_2_16_2"/><i><font color="Green">E218</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:70_2_16_2"/><i><font color="Green">E219</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><a NAME="E6:70_2_16_2"/><i><font color="Green">E220</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E7:70_2_16_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T13">SCMRING2:13</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E8:70_2_16_2"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_2_1"/><i><font color="Green">E221</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_2_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_2_1"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/><a NAME="E5:70_2_16_2_1"/><b>then </b><i><font color="Green">E222</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_2_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_1_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_2_1_1_1"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_2_1_1_1"/><b>then </b><i><font color="Green">E224</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><a NAME="E3:70_2_16_2_1_1_1"/><i><font color="Green">E225</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><a NAME="E4:70_2_16_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , , </i>;<br/><b>hence </b><a NAME="E5:70_2_16_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_1_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_2_1_1_2"/>
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_2_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, <a class="ref" href="scmring4.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E10:70_2_16_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E11:70_2_16_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_2_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/><b>assume </b><a NAME="E1:70_2_16_2_2"/><i><font color="Green">E226</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_2_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_2_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_2_2_1_1"/>
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_2_2_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_2_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_2_2_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_2_2_1_2"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_2_2_1_2"/><b>then </b><i><font color="Green">E228</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><a NAME="E3:70_2_16_2_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_2_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E13:70_2_16_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E14:70_2_16_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3"><b>suppose </b></a><a NAME="E1:70_2_16_3"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:70_2_16_3"/><i><font color="Green">E229</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T18">SCMRING3:18</a></i>;<br/><a NAME="E4:70_2_16_3"/><i><font color="Green">E230</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:70_2_16_3"/><i><font color="Green">E231</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><a NAME="E6:70_2_16_3"/><i><font color="Green">E232</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font>
 <b>by </b><i/>;<br/><a NAME="E7:70_2_16_3"/><i><font color="Green">E233</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E8:70_2_16_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E9:70_2_16_3"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_3_1"/><i><font color="Green">E234</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_3_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_3_1"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/><a NAME="E5:70_2_16_3_1"/><b>then </b><i><font color="Green">E235</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_3_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_1_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_3_1_1_1"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_3_1_1_1"/><b>then </b><i><font color="Green">E237</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><a NAME="E3:70_2_16_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><a NAME="E4:70_2_16_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , , , , </i>;<br/><b>hence </b><a NAME="E5:70_2_16_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_1_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_3_1_1_2"/>
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_3_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_3_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E11:70_2_16_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E12:70_2_16_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_3_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/><b>assume </b><a NAME="E1:70_2_16_3_2"/><i><font color="Green">E238</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_3_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_2_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_3_2_1_1"/><i><font color="Green">E239</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_3_2_1_1"/><b>then </b><i><font color="Green">E240</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><a NAME="E3:70_2_16_3_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_3_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_3_2_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_3_2_1_2"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_3_2_1_2"/><b>then </b><i><font color="Green">E242</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><a NAME="E3:70_2_16_3_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_3_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E14:70_2_16_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E15:70_2_16_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4"><b>suppose </b></a><a NAME="E1:70_2_16_4"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:70_2_16_4"/><i><font color="Green">E243</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T19">SCMRING3:19</a></i>;<br/><a NAME="E4:70_2_16_4"/><i><font color="Green">E244</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:70_2_16_4"/><i><font color="Green">E245</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><a NAME="E6:70_2_16_4"/><i><font color="Green">E246</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font>
 <b>by </b><i/>;<br/><a NAME="E7:70_2_16_4"/><i><font color="Green">E247</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E8:70_2_16_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E9:70_2_16_4"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_4_1"/><i><font color="Green">E248</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_4_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_4_1"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/><a NAME="E5:70_2_16_4_1"/><b>then </b><i><font color="Green">E249</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_4_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_1_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_4_1_1_1"/><i><font color="Green">E250</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_4_1_1_1"/><b>then </b><i><font color="Green">E251</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><a NAME="E3:70_2_16_4_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><a NAME="E4:70_2_16_4_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , , , , <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>;<br/><b>hence </b><a NAME="E5:70_2_16_4_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_1_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_4_1_1_2"/>
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_4_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_4_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E11:70_2_16_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E12:70_2_16_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_4_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/><b>assume </b><a NAME="E1:70_2_16_4_2"/><i><font color="Green">E252</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_4_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_2_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_4_2_1_1"/><i><font color="Green">E253</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_4_2_1_1"/><b>then </b><i><font color="Green">E254</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><a NAME="E3:70_2_16_4_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_4_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_4_2_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_4_2_1_2"/><i><font color="Green">E255</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_4_2_1_2"/><b>then </b><i><font color="Green">E256</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><a NAME="E3:70_2_16_4_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_4_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E14:70_2_16_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E15:70_2_16_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5"><b>suppose </b></a><a NAME="E1:70_2_16_5"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:70_2_16_5"/><i><font color="Green">E257</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T20">SCMRING3:20</a></i>;<br/><a NAME="E4:70_2_16_5"/><i><font color="Green">E258</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:70_2_16_5"/><i><font color="Green">E259</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><a NAME="E6:70_2_16_5"/><i><font color="Green">E260</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font>
 <b>by </b><i/>;<br/><a NAME="E7:70_2_16_5"/><i><font color="Green">E261</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E8:70_2_16_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E9:70_2_16_5"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_5_1"/><i><font color="Green">E262</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_5_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_5_1"/>
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T62">AMI_5:62</a></i>;<br/><a NAME="E5:70_2_16_5_1"/><b>then </b><i><font color="Green">E263</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_5_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_1_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_5_1_1_1"/><i><font color="Green">E264</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_5_1_1_1"/><b>then </b><i><font color="Green">E265</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><a NAME="E3:70_2_16_5_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><a NAME="E4:70_2_16_5_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , , , , </i>;<br/><b>hence </b><a NAME="E5:70_2_16_5_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E27"><i><font color="Green">Lemma94</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_1_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_5_1_1_2"/>
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_5_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_5_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E11:70_2_16_5"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E12:70_2_16_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_5_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/><b>assume </b><a NAME="E1:70_2_16_5_2"/><i><font color="Green">E266</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_5_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_2_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_5_2_1_1"/><i><font color="Green">E267</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_5_2_1_1"/><b>then </b><i><font color="Green">E268</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><a NAME="E3:70_2_16_5_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_5_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_5_2_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_5_2_1_2"/><i><font color="Green">E269</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_5_2_1_2"/><b>then </b><i><font color="Green">E270</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><a NAME="E3:70_2_16_5_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_5_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E14:70_2_16_5"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E15:70_2_16_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6"><b>suppose </b></a><a NAME="E1:70_2_16_6"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:70_2_16_6"/><i><font color="Green">E271</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T21">SCMRING3:21</a></i>;<br/><a NAME="E4:70_2_16_6"/><i><font color="Green">E272</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:70_2_16_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><b>hence </b><a NAME="E6:70_2_16_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, , <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E7:70_2_16_6"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_6_1"/><i><font color="Green">E273</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_6_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_6_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_1_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_6_1_1_1"/><i><font color="Green">E274</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">r</font>
<b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_1_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_6_1_1_2"/>
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_6_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_6_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E9:70_2_16_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E10:70_2_16_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_6_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/><b>assume </b><a NAME="E1:70_2_16_6_2"/><i><font color="Green">E275</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_6_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_2_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_6_2_1_1"/>
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_6_2_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> )
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><b>hence </b><a NAME="E3:70_2_16_6_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E28"><i><font color="Green">Lemma95</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_6_2_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_6_2_1_2"/><i><font color="Green">E276</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:70_2_16_6_2_1_2"/><b>then </b><i><font color="Green">E277</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><a NAME="E3:70_2_16_6_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_6_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E12:70_2_16_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E13:70_2_16_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_7"><b>suppose </b></a><a NAME="E1:70_2_16_7"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:70_2_16_7"/><i><font color="Green">E278</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T22">SCMRING3:22</a></i>;<br/><a NAME="E4:70_2_16_7"/><i><font color="Green">E279</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
<font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a></i>
;<br/><b>hence </b><a NAME="E6:70_2_16_7"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_7_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/><b>assume </b><a NAME="E1:70_2_16_7_2"/><i><font color="Green">E280</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_7_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_7_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>;<br/><b>hence </b><a NAME="E5:70_2_16_7_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div><a NAME="E8:70_2_16_7"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E9:70_2_16_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_7_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_7_3"/><i><font color="Green">E281</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E3:70_2_16_7_3"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_7_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, </i>;<br/></div><b>end;</b></div><a NAME="E11:70_2_16_7"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E12:70_2_16_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8"><b>suppose </b></a><a NAME="E1:70_2_16_8"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:70_2_16_8"/><i><font color="Green">E282</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T23">SCMRING3:23</a></i>;<br/><a NAME="E4:70_2_16_8"/><i><font color="Green">E283</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, </i>;<br/><a NAME="E5:70_2_16_8"/><i><font color="Green">E284</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font>
 <b>by </b><i/>;<br/><div><i><font color="Green">E285</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_8_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_1_1_1"><b>case </b></a><a NAME="E1:70_2_16_8_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_2_16_8_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_1_1_2"><b>case </b></a><a NAME="E1:70_2_16_8_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_2_16_8_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, <a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><i><font color="Green">E286</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_8_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_8_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_2_1_1"><b>case </b></a><a NAME="E1:70_2_16_8_2_1_1"/><i><font color="Green">E287</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:70_2_16_8_2_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_2_1_2"><b>case </b></a><a NAME="E1:70_2_16_8_2_1_2"/><i><font color="Green">E288</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:70_2_16_8_2_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_8_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_2_16_8_3_1"/>
( <font color="Maroon">loc</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> or <font color="Maroon">loc</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_3_1_1"><b>suppose </b></a><a NAME="E1:70_2_16_8_3_1_1"/>
<font color="Maroon">loc</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_2_16_8_3_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="scmring4.html#T9" target="_self">Th9</a>, , <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, , , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_2_16_8_3_1_2"><b>suppose </b></a><a NAME="E1:70_2_16_8_3_1_2"/>
<font color="Maroon">loc</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:70_2_16_8_3_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T11" target="_self">Th11</a>, <a class="ref" href="scmring4.html#T31" target="_self">Th31</a>, , <a class="ref" href="scmring4.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:70_2_16_8"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp;  <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="scmring4.html#T22" target="_self">Th22</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_8_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_8_4"/><i><font color="Green">E289</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:70_2_16_8_4"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i/>;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E4:70_2_16_8_4"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self">Th24</a>, <a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/><b>hence </b><a NAME="E5:70_2_16_8_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmring4.html#T20" target="_self">Th20</a>, </i>;<br/></div><b>end;</b></div><a NAME="E11:70_2_16_8"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E12:70_2_16_8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring4.html#T13" target="_self">Th13</a>, <a class="txt" href="scmring4.html#E12:70"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmring4.html#E13:70"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2_16_8_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:70_2_16_8_5"/><i><font color="Green">E290</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">d</font> = <font color="Maroon">x</font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> <b>by </b><i>, <a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/><a NAME="E3:70_2_16_8_5"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="scmring4.html#T26" target="_self">Th26</a>, <a class="ref" href="scmring4.html#T29" target="_self">Th29</a>, <a class="ref" href="scmring4.html#T33" target="_self">Th33</a>, <a class="ref" href="scmring4.html#T34" target="_self">Th34</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/><b>hence </b><a NAME="E4:70_2_16_8_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T21" target="_self">Th21</a>, </i>;<br/></div><b>end;</b></div><a NAME="E14:70_2_16_8"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring4.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E15:70_2_16_8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E16:70"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, <a class="ref" href="scmring4.html#T10" target="_self">Th10</a>);<br/></i>
<b>hence </b><a NAME="E17:70"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> &amp;  <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <span class="p3">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  )
 ;<br/>


</div>
