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<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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a><br/>

<b>reconsider </b><font color="Maroon" title="c7">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="c8">I</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0;<br/>
<i><font color="Green" title="E40">A1</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c7">S</font> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a> 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>
<br/>.= 
 <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c9">Es</font> =  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0</span>)</span>,<font color="Maroon" title="c6">s</font> as   <a href="scmpds_1.html#NM1" title="SCMPDS_1:NM.1">SCMPDS-State</a> ;<br/>
<div><i><font color="Green" title="E41">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:86_2"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font>
 ;<br/><a NAME="E2:86_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E3:86_2"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
 <b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">m</font> = <font color="Maroon" title="c10">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a>  <b>by </b><i><a class="txt" href="scmpds_2.html#E1:86_2"><i><font color="Green" title="E42">A3</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_2_1"/>
( <font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  or <font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  or <font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  )
 </span><b>by </b><i><a class="ref" href="scmpds_1.html#T14" title="SCMPDS_1:th.14">SCMPDS_1:14</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_2_1_1"><b>suppose </b></a><a NAME="E1:86_2_1_1"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c12">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:86_2_1_1"/><i><font color="Green" title="E44">A5</font></i>: 
( <font color="Maroon" title="c12">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c6">s</font>,0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" target="_self" title="SCMPDS_2:def.20">Def20</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">n</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  ;<br/><b>consider </b><font color="Maroon" title="c14">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:86_2_1_1"/><i><font color="Green" title="E45">A6</font></i>: 
<font color="Maroon" title="c13">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">k</font>
 ;<br/><a NAME="E7:86_2_1_1"/><i><font color="Green" title="E46">X</font></i>: 
<font color="Maroon" title="c13">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/><b>thus </b><font color="Maroon" title="c9">Es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c14">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_2.html#E1:86_2_1_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="scmpds_2.html#E3:86_2_1_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="txt" href="scmpds_2.html#E6:86_2_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="scmpds_2.html#T66" target="_self" title="SCMPDS_2:th.66">Th66</a>, <a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Tx</a></i>
<br/>.= 
<font color="Maroon" title="c14">k</font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E6:86_2_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a>, <a class="txt" href="scmpds_2.html#E7:86_2_1_1"><i><font color="Green" title="E46">X</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<b>by </b><i><a class="txt" href="scmpds_2.html#E1:86_2_1_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="scmpds_2.html#E6:86_2_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="scmpds_2.html#T6" target="_self" title="SCMPDS_2:th.6">Tx</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_2_1_2"><b>suppose </b></a><a NAME="E1:86_2_1_2"/>
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:86_2_1_2"/><b>then </b>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">d</font> = <font color="Maroon" title="c10">x</font> as    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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>thus </b><font color="Maroon" title="c9">Es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<font color="Maroon" title="c6">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c12">d</font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T66" target="_self" title="SCMPDS_2:th.66">Th66</a></i>
<br/>.= 
<font color="Maroon" title="c7">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>

;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_2_1_3"><b>suppose </b></a><a NAME="E1:86_2_1_3"/>
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:86_2_1_3"/><b>then </b>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">v</font> = <font color="Maroon" title="c10">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  ;<br/><b>reconsider </b><font color="Maroon" title="c13">I0</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0 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="c14">i</font> = 0 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">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 href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0</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="c13">I0</font>,<font color="Maroon" title="c7">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> <font color="Maroon" title="c7">S</font>,<span class="p1">(<span class="default"><a href="scmpds_1.html#K8" title="SCMPDS_1:func.8">jump_address</a> <font color="Maroon" title="c7">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">I0</font> <a href="scmpds_1.html#K11" title="SCMPDS_1:func.11">const_INT</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
;<br/><b>hence </b><font color="Maroon" title="c9">Es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<font color="Maroon" title="c7">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">v</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c7">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>

;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">Es</font> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a> 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>
<br/>.= 
 <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E6:86"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0</span>)</span>,<font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E2:86"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="scmpds_2.html#E4:86"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


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