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<div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="scmpds_2.html#M1" target="_self">Int_position</a> ;<br/>







<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <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="scmpds_2.html#D2" target="_self">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> =  <a href="scmpds_2.html#K12" target="_self">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="scmpds_1.html#K1">SCMPDS-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="scmpds_1.html#NM1">SCMPDS-State</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> =  <a href="scmpds_1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="scmpds_1.html#K6">.</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K16">P33const</a> </span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = 8 as    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<a NAME="E5:71"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>11</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>16</sub></font>,<span class="p2"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 
;<br/>
<a NAME="E6:71"/><i><font color="Green">E30</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_1.html#K3">IC</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T7" target="_self">Th7</a></i>;<br/>
<i><font color="Green">E31</font></i>:  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" target="_self">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font> = 
 <a href="scmpds_1.html#K24">SCM-Exec-Res</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T56" target="_self">Th56</a></i>
<br/>.= 
 <a href="scmpds_1.html#K4">SCM-Chg</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="scmpds_1.html#K6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K16">P33const</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="scmpds_1.html#K3">IC</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E5:71"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_1.html#D24">SCMPDS_1:def 24</a></i>
;<br/>
<a NAME="E8:71"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K16">P33const</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E5:71"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_1.html#T36">SCMPDS_1:36</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="scmpds_2.html#K12" target="_self">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>6</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> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> </span>)</span> = 
 <a href="ami_2.html#K15">Next</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K3">IC</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_1.html#T26">SCMPDS_1:26</a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:71"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmpds_2.html#T55" target="_self">Th55</a></i>
;<br/>

<a NAME="E10:71"/><i><font color="Green">E33</font></i>: 
 <a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E8:71"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_1.html#D8">SCMPDS_1:def 8</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="scmpds_2.html#K12" target="_self">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="scmpds_2.html#K2" target="_self">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" target="_self">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="scmpds_1.html#K6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K16">P33const</a> </span>)</span></span>)</span></span>)</span> <a href="scmpds_1.html#K6">.</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmpds_2.html#E10:71"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_1.html#T27">SCMPDS_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" target="_self">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E8:71"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmpds_2.html#E10:71"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_1.html#T30">SCMPDS_1:30</a></i>
;<br/>

<b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="scmpds_2.html#M1" target="_self">Int_position</a> ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <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="scmpds_2.html#D2" target="_self">Def2</a></i>;<br/>
<b>assume </b><a NAME="E13:71"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3" target="_self">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>
 ;<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="scmpds_2.html#K12" target="_self">AddTo</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>17</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5">SCM-Chg</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="scmpds_1.html#K6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7">Address_Add</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmpds_1.html#K16">P33const</a> </span>)</span></span>)</span></span>)</span> <a href="scmpds_1.html#K6">.</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_1.html#T27">SCMPDS_1:27</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E10:71"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmpds_2.html#E13:71"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_1.html#T31">SCMPDS_1:31</a></i>
;<br/>


</div>
