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<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">a</font> be    <a href="scmring2.html#M1" target="_self">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">b</font> be    <a href="scmring2.html#M1" target="_self">Data-Location</a> of <font color="Maroon">R</font>;<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" target="_self">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/>







<b>reconsider </b><font color="Maroon">I</font> =  <a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="scmring1.html#K1">SCM-Instr</a> <font color="Maroon">R</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">S</font> = <font color="Maroon">s</font> as   <a href="scmring1.html#NM1">SCM-State</a> of <font color="Maroon">R</font> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">i</font> = 2 as    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 8 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<a NAME="E4:24"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 
;<br/>
<a NAME="E5:24"/><i><font color="Green">E35</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="scmring1.html#K3">IC</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:24"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  &amp; <font color="Maroon">b</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  )
 
<b>by </b><i/>;<br/>
<i><font color="Green">E38</font></i>:  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">s</font> = 
 <a href="scmring1.html#K15">SCM-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font>
<b>by </b><i/>
<br/>.= 
 <a href="scmring1.html#K4">SCM-Chg</a> <span class="p1">(<span class="default"><a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K15">Next</a> <span class="p2">(<span class="default"><a href="scmring1.html#K3">IC</a> <font color="Maroon">S</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring1.html#D14">SCMRING1:def 14</a></i>
;<br/>
<a NAME="E8:24"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">I</font> <a href="scmring1.html#K8">address_2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 
<b>by </b><i>, , <a class="ref" href="scmring1.html#T17">SCMRING1:17</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">s</font></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" target="_self">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> 0
<b>by </b><i/>
<br/>.= 
 <a href="ami_2.html#K15">Next</a> <span class="p1">(<span class="default"><a href="scmring1.html#K3">IC</a> <font color="Maroon">S</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring1.html#T10">SCMRING1:10</a></i>
<br/>.= 
 <a href="scmring2.html#K11" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i>, </i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="scmring1.html#T11">SCMRING1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring1.html#T14">SCMRING1:14</a></i>
;<br/>

<b>let </b><font color="Maroon">c</font> be    <a href="scmring2.html#M1" target="_self">Data-Location</a> of <font color="Maroon">R</font>;<br/>

<b>assume </b><a NAME="E11:24"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E12:24"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmring1.html#K6">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmring1.html#T11">SCMRING1:11</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c</font>
<b>by </b><i>, , , <a class="ref" href="scmring1.html#T15">SCMRING1:15</a></i>
;<br/><br/>


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