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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="scmring2.html#M1" target="_self">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span>;<br/>







<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="scmring1.html#K1">SCM-Instr</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self">Def1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="scmring1.html#NM1">SCM-State</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self">Def1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring1.html#K6">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = 1 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="E4:23"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 
;<br/>
<a NAME="E5:23"/><i><font color="Green">E18</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmring1.html#K3">IC</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="scmring2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E6:23"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></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><a class="ref" href="scmring2.html#T1" target="_self">Th1</a></i>;<br/>
<i><font color="Green">E20</font></i>:  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="scmring1.html#K15">SCM-Exec-Res</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="scmring2.html#T12" target="_self">Th12</a></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">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring1.html#K6">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K8">address_2</a> </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">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring2.html#E6:23"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmring1.html#D14">SCMRING1:def 14</a></i>
;<br/>
<a NAME="E8:23"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K7">address_1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K8">address_2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="scmring2.html#E4:23"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmring2.html#E6:23"><i><font color="Green">E19</font></i></a>, <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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 0
<b>by </b><i><a class="ref" href="scmring2.html#T9" target="_self">Th9</a></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">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring2.html#E7:23"><i><font color="Green">E20</font></i></a>, <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">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring2.html#E5:23"><i><font color="Green">E18</font></i></a>, <a class="ref" href="scmring2.html#T11" target="_self">Th11</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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring1.html#K6">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="scmring2.html#E6:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmring2.html#E7:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmring1.html#T11">SCMRING1:11</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmring2.html#E8:23"><i><font color="Green">E21</font></i></a>, <a class="ref" href="scmring1.html#T14">SCMRING1:14</a></i>
;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="scmring2.html#M1" target="_self">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E11:23"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E12:23"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>9</sub></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><a class="ref" href="scmring2.html#T1" target="_self">Th1</a></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4" target="_self">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring1.html#K6">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring1.html#K8">address_2</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmring2.html#E7:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmring1.html#T11">SCMRING1:11</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmring2.html#K3" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmring2.html#E8:23"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmring2.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmring2.html#E12:23"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scmring1.html#T15">SCMRING1:15</a></i>
;<br/><br/>


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