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

<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E58">A1</font></i>: 
not <font color="Maroon" title="c2">R</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>, <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:75"/><i><font color="Green" title="E59">A2</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">p</font>
 <b>and </b><br/><a NAME="E3:75"/><i><font color="Green" title="E60">A3</font></i>: 
<font color="Maroon" title="c4">F</font> is <a href="ami_1.html#V17" title="AMI_1:attr.17">data-only</a>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:75_1"/><i><font color="Green" title="E61">A4</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a> <font color="Maroon" title="c4">F</font>
 ;<br/><b>thus </b><a NAME="E2:75_1"/>
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a> <font color="Maroon" title="c4">F</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a><br/>

<b>assume </b><a NAME="E1:75_1_1"/><i><font color="Green" title="E62">A5</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">F</font>
 ;<br/>

<a NAME="E2:75_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">s</font> = <font color="Maroon" title="c5">x</font> as  <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="txt" href="scmring4.html#E3:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="scmring4.html#E1:75_1_1"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="ami_1.html#D51" title="AMI_1:def.51">AMI_1:def 51</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">s</font>
;<br/>

<b>thus </b><a NAME="E4:75_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">s1</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span><b> such that </b><br/><a NAME="E6:75_1_1"/><i><font color="Green" title="E63">A6</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s1</font> &amp; <font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="scmring4.html#E1:75_1"><i><font color="Green" title="E61">A4</font></i></a>, <a class="txt" href="scmring4.html#E1:75_1_1"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Fs1</font> = <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="ref" href="ami_1.html#T98" title="AMI_1:th.98">AMI_1:98</a></i>;<br/>
<a NAME="E8:75_1_1"/><i><font color="Green" title="E64">A7</font></i>: 
<font color="Maroon" title="c8">Fs1</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="scmring4.html#E1:75_1_1"><i><font color="Green" title="E62">A5</font></i></a>, <a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="ref" href="ami_1.html#D51" title="AMI_1:def.51">AMI_1:def 51</a></i>;<br/>
<a NAME="E9:75_1_1"/><b>then </b><i><font color="Green" title="E65">A8</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></i>;<br/>
<a NAME="E10:75_1_1"/><i><font color="Green" title="E66">A9</font></i>: 
<span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="scmring4.html#T57" target="_self" title="SCMRING4:th.57">Th57</a></i>;<br/>
<a NAME="E11:75_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E12:75_1_1"/><b>then </b><i><font color="Green" title="E67">A10</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E13:75_1_1"/>
<span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="scmring4.html#E10:75_1_1"><i><font color="Green" title="E66">A9</font></i></a>, <a class="ref" href="scmring4.html#T60" target="_self" title="SCMRING4:th.60">Th60</a>, <a class="ref" href="scmring4.html#T64" target="_self" title="SCMRING4:th.64">Th64</a></i>;<br/>

 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="scmring4.html#E12:75_1_1"><i><font color="Green" title="E67">A10</font></i></a>, <a class="ref" href="scmring4.html#T65" target="_self" title="SCMRING4:th.65">Th65</a></i>
<br/>.= 
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="scmring4.html#T57" target="_self" title="SCMRING4:th.57">Th57</a></i>
;<br/>
<b>hence </b><a NAME="E15:75_1_1"/>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E6:75_1_1"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="scmring4.html#E8:75_1_1"><i><font color="Green" title="E64">A7</font></i></a>, <a class="txt" href="scmring4.html#E9:75_1_1"><i><font color="Green" title="E65">A8</font></i></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></i>;<br/>


</div><b>end;</b></div></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:75"/><i><font color="Green" title="E61">A11</font></i>: 
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">computes</a> <font color="Maroon" title="c4">F</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a><br/>

<b>assume </b><a NAME="E6:75"/><i><font color="Green" title="E62">A12</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">F</font>
 ;<br/>

<a NAME="E7:75"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">s</font> = <font color="Maroon" title="c5">x</font> as  <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="txt" href="scmring4.html#E3:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="scmring4.html#E6:75"><i><font color="Green" title="E62">A12</font></i></a>, <a class="ref" href="ami_1.html#D51" title="AMI_1:def.51">AMI_1:def 51</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">s</font>
;<br/>

<b>thus </b><a NAME="E9:75"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">s1</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span><b> such that </b><br/><a NAME="E11:75"/><i><font color="Green" title="E63">A13</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="scmring4.html#E5:75"><i><font color="Green" title="E61">A11</font></i></a>, <a class="txt" href="scmring4.html#E6:75"><i><font color="Green" title="E62">A12</font></i></a>, <a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Fs1</font> = <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="ami_1.html#T98" title="AMI_1:th.98">AMI_1:98</a></i>;<br/>
<a NAME="E13:75"/><i><font color="Green" title="E64">A14</font></i>: 
<font color="Maroon" title="c8">Fs1</font> is <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="scmring4.html#E6:75"><i><font color="Green" title="E62">A12</font></i></a>, <a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="ami_1.html#D51" title="AMI_1:def.51">AMI_1:def 51</a></i>;<br/>
<a NAME="E14:75"/><b>then </b><i><font color="Green" title="E65">A15</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></i>;<br/>
<a NAME="E15:75"/><i><font color="Green" title="E66">A16</font></i>: 
<span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="scmring4.html#T57" target="_self" title="SCMRING4:th.57">Th57</a></i>;<br/>
<a NAME="E16:75"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E17:75"/><b>then </b><i><font color="Green" title="E67">A17</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E18:75"/><b>then </b><i><font color="Green" title="E68">A18</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="txt" href="scmring4.html#E15:75"><i><font color="Green" title="E66">A16</font></i></a>, <a class="ref" href="scmring4.html#T64" target="_self" title="SCMRING4:th.64">Th64</a></i>;<br/>
<b>hence </b><a NAME="E19:75"/>
<font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="txt" href="scmring4.html#E15:75"><i><font color="Green" title="E66">A16</font></i></a>, <a class="txt" href="scmring4.html#E17:75"><i><font color="Green" title="E67">A17</font></i></a>, <a class="ref" href="scmring4.html#T60" target="_self" title="SCMRING4:th.60">Th60</a></i>;<br/>

<a NAME="E20:75"/><i><font color="Green" title="E69">A19</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="txt" href="scmring4.html#E15:75"><i><font color="Green" title="E66">A16</font></i></a>, <a class="txt" href="scmring4.html#E17:75"><i><font color="Green" title="E67">A17</font></i></a>, <a class="txt" href="scmring4.html#E18:75"><i><font color="Green" title="E68">A18</font></i></a>, <a class="ref" href="scmring4.html#T60" target="_self" title="SCMRING4:th.60">Th60</a></i>;<br/>
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c7">s1</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="scmring4.html#T57" target="_self" title="SCMRING4:th.57">Th57</a></i>
<br/>.= 
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="scmring4.html#E17:75"><i><font color="Green" title="E67">A17</font></i></a>, <a class="txt" href="scmring4.html#E18:75"><i><font color="Green" title="E68">A18</font></i></a>, <a class="txt" href="scmring4.html#E20:75"><i><font color="Green" title="E69">A19</font></i></a>, <a class="ref" href="scmring4.html#T65" target="_self" title="SCMRING4:th.65">Th65</a></i>
;<br/>
<b>hence </b><a NAME="E22:75"/>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E11:75"><i><font color="Green" title="E63">A13</font></i></a>, <a class="txt" href="scmring4.html#E13:75"><i><font color="Green" title="E64">A14</font></i></a>, <a class="txt" href="scmring4.html#E14:75"><i><font color="Green" title="E65">A15</font></i></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></i>;<br/>


</div>
