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

<span class="kw">let </span><font color="Maroon" title="c1">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Olive" title="b3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b3">s</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Olive" title="b3">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span> &amp; ( for <font color="Olive" title="b4">c</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Olive" title="b3">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b4">c</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c3">b</font></span>)</span> &amp; ( for <font color="Olive" title="b2">c</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b2">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b2">c</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c3">b</font></span>)</span> &amp; ( for <font color="Olive" title="b1">c</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font> ) )</span><br/>







<a NAME="E1:23"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T1" target="_self" title="SCMRING2:th.1">Th1</a></span>;<br/>
<a NAME="E2:23"/><span class="lab"><font color="Green" title="E15">Y</font></span>: 
the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="scmring1.html#K2" title="SCMRING1:func.2">SCM-OK</a> <font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">S</font> = <font color="Maroon" title="c4">s</font> as   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E15">Y</font></span></a>, <a class="ref" href="pboole.html#T155" title="PBOOLE:th.155">PBOOLE:155</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">I</font> =  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">S1</font> =  <a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">i</font> = 2 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></span>;<br/>
<a NAME="E6:23"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c5">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>;<br/>
<a NAME="E7:23"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T1" target="_self" title="SCMRING2:th.1">Th1</a></span>;<br/>
<span class="lab"><font color="Green" title="E18">A4</font></span>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font> = 
 <a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T12" target="_self" title="SCMRING2:th.12">Th12</a></span>
<br/>.= 
 <a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p2">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></span>
;<br/>
<a NAME="E9:23"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">i</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
;<br/>
<a NAME="E10:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="scmring1.html#T17" title="SCMRING1:th.17">SCMRING1:17</a></span>;<br/>
<a NAME="E11:23"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c6">I</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="scmring1.html#T17" title="SCMRING1:th.17">SCMRING1:17</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>
<br/>.= 
 <a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="scmring1.html#T10" title="SCMRING1:th.10">SCMRING1:10</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c3">b</font></span>)</span> &amp; ( for <font color="Olive" title="b1">c</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font> ) )</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="scmring1.html#T11" title="SCMRING1:th.11">SCMRING1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c3">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="scmring1.html#T14" title="SCMRING1:th.14">SCMRING1:14</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">c</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">c</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">c</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> implies <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font> )</span><br/>

<span class="kw">assume </span><a NAME="E14:23"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font></span><br/>

<a NAME="E15:23"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c9">c</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T1" target="_self" title="SCMRING2:th.1">Th1</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="scmring1.html#T11" title="SCMRING1:th.11">SCMRING1:11</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c9">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="scmring1.html#T15" title="SCMRING1:th.15">SCMRING1:15</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
