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<div class="add">

<b>let </b><font color="Maroon" title="c6">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c7">k1</font>, <font color="Maroon" title="c8">k2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>let </b><font color="Maroon" title="c9">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/>







<b>reconsider </b><font color="Maroon" title="c10">mk</font> = <font color="Maroon" title="c9">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="scmpds_2.html#D2" target="_self" title="SCMPDS_2:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">I</font> =  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">S</font> = <font color="Maroon" title="c6">s</font> as   <a href="scmpds_1.html#NM1" title="SCMPDS_1:NM.1">SCMPDS-State</a> ;<br/>
<b>set </b><font color="Maroon" title="c13">A1</font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">k1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/>
<b>set </b><font color="Maroon" title="c14">A2</font> =  <a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c15">S1</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c12">S</font>,<span class="p1">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">i</font> = 8 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> 14 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10" title="GR_CY_1:th.10">GR_CY_1:10</a></i>;<br/>
<a NAME="E5:71"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c11">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="c16">i</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c10">mk</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
;<br/>
<i><font color="Green" title="E26">A2</font></i>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font></span>)</span>,<font color="Maroon" title="c6">s</font> = 
 <a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c11">I</font>,<font color="Maroon" title="c12">S</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#D25" title="SCMPDS_1:def.25">SCMPDS_1:def 25</a></i>
<br/>.= 
 <a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c12">S</font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c12">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c12">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E5:71"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
;<br/>
<a NAME="E7:71"/><i><font color="Green" title="E27">A3</font></i>: 
( <font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">mk</font> &amp; <font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">k1</font> &amp; <font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">k2</font> )
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E5:71"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="scmpds_1.html#T36" title="SCMPDS_1:th.36">SCMPDS_1:36</a></i>;<br/>
<b>thus </b><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="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font></span>)</span>,<font color="Maroon" title="c6">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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> = 
 <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c12">S</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:71"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Th6</a>, <a class="ref" href="scmpds_1.html#T26" title="SCMPDS_1:th.26">SCMPDS_1:26</a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Th6</a>, <a class="ref" href="scmpds_2.html#T55" target="_self" title="SCMPDS_2:th.55">Th55</a></i>
;<br/>

<b>thus </b><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="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font></span>)</span>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c7">k1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c12">S</font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c12">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p1">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:71"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="scmpds_1.html#T27" title="SCMPDS_1:th.27">SCMPDS_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c7">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">k2</font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="scmpds_1.html#T30" title="SCMPDS_1:th.30">SCMPDS_1:30</a></i>
;<br/>

<b>let </b><font color="Maroon" title="c17">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c18">mn</font> = <font color="Maroon" title="c17">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="scmpds_2.html#D2" target="_self" title="SCMPDS_2:def.2">Def2</a></i>;<br/>
<b>assume </b><a NAME="E11:71"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c17">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<font color="Maroon" title="c7">k1</font>
 ;<br/>

<b>thus </b><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="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c7">k1</font>,<font color="Maroon" title="c8">k2</font></span>)</span>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">c</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c12">S</font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c12">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c12">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">I</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <font color="Maroon" title="c18">mn</font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:71"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="scmpds_1.html#T27" title="SCMPDS_1:th.27">SCMPDS_1:27</a></i>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">c</font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E7:71"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="scmpds_2.html#E11:71"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="scmpds_1.html#T31" title="SCMPDS_1:th.31">SCMPDS_1:31</a></i>
;<br/>


</div>
