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<b>let </b><font color="Maroon" title="c6">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">l</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b2">l</font></span><br/><b>let </b><font color="Maroon" title="c7">i</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">l</font></span><br/><b>let </b><font color="Maroon" title="c8">l</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">l</font></span><br/>





<b>reconsider </b><font color="Maroon" title="c9">c</font> = <font color="Maroon" title="c7">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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="c10">S</font> = <font color="Maroon" title="c6">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">l'</font> = <font color="Maroon" title="c8">l</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">NAT</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span>}</span>  or <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">d1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font>,<font color="Olive" title="b3">k2</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I1</font> is    <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, <font color="Olive" title="b2">d2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d3</font>,<font color="Olive" title="b3">k3</font>,<font color="Olive" title="b4">k4</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> where <font color="Olive" title="b1">I2</font> is    <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, <font color="Olive" title="b2">d3</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k3</font>, <font color="Olive" title="b4">k4</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  or <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I3</font>,<span class="p3"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Olive" title="b2">d4</font>,<font color="Olive" title="b3">d5</font>,<font color="Olive" title="b4">k5</font>,<font color="Olive" title="b5">k6</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I3</font> is    <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, <font color="Olive" title="b2">d4</font>, <font color="Olive" title="b3">d5</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b4">k5</font>, <font color="Olive" title="b5">k6</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 </span><b>by </b><i><a class="txt" href="scmpds_2.html#E16"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_1"><b>case </b></a><a NAME="E1:89_1_1_1"/>
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">k1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:89_1_1_1"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c9">c</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"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c12">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K8" title="SCMPDS_1:func.8">jump_address</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K11" title="SCMPDS_1:func.11">const_INT</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_2"><b>case </b></a><a NAME="E1:89_1_1_2"/>
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">d1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:89_1_1_2"/><i><font color="Green" title="E58">A2</font></i>: 
<font color="Maroon" title="c9">c</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">1,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c12">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><b>set </b><font color="Maroon" title="c13">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K21" title="SCMPDS_1:func.21">PopInstrLoc</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_2"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K10" title="SCMPDS_1:func.10">address_1</a> </span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_3"><b>case </b></a><a NAME="E1:89_1_1_3"/>
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font>,<font color="Olive" title="b3">k2</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I1</font> is    <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, <font color="Olive" title="b2">d2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">I1</font> being    <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, <font color="Maroon" title="c13">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c14">k1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:89_1_1_3"/><i><font color="Green" title="E58">A3</font></i>: 
( <font color="Maroon" title="c9">c</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="c12">I1</font>,<span class="p2"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">k1</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 ;<br/><b>set </b><font color="Maroon" title="c15">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_1_1_3_1_1"/>
( <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E3:89_1_1_3"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_3_1_1_1"><b>case </b></a><a NAME="E1:89_1_1_3_1_1_1"/>
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_3"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_3_1_1_2"><b>case </b></a><a NAME="E1:89_1_1_3_1_1_2"/><i><font color="Green" title="E59">A4</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c16">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_3"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="#E1:89_1_1_3_1_1_2"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K12" title="SCMPDS_1:func.12">P21address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K13" title="SCMPDS_1:func.13">P22const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:89_1_1_3"/>
<span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4"><b>case </b></a><a NAME="E1:89_1_1_4"/>
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d3</font>,<font color="Olive" title="b3">k3</font>,<font color="Olive" title="b4">k4</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> where <font color="Olive" title="b1">I2</font> is    <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, <font color="Olive" title="b2">d3</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k3</font>, <font color="Olive" title="b4">k4</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">I1</font> being    <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, <font color="Maroon" title="c13">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c14">k1</font>, <font color="Maroon" title="c15">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:89_1_1_4"/><i><font color="Green" title="E58">A5</font></i>: 
( <font color="Maroon" title="c9">c</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="c12">I1</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">k1</font>,<font color="Maroon" title="c15">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> &amp; <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_1_1_4_1_1"/>
( <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1_1"><b>case </b></a><a NAME="E1:89_1_1_4_1_1_1"/>
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K8" title="SCMPDS_1:func.8">jump_address</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1_2"><b>case </b></a><a NAME="E1:89_1_1_4_1_1_2"/>
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K5" title="XXREAL_0:func.5">IFGT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K8" title="SCMPDS_1:func.8">jump_address</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1_3"><b>case </b></a><a NAME="E1:89_1_1_4_1_1_3"/>
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K5" title="XXREAL_0:func.5">IFGT</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p4">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K8" title="SCMPDS_1:func.8">jump_address</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1_4"><b>case </b></a><a NAME="E1:89_1_1_4_1_1_4"/><i><font color="Green" title="E59">A6</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c16">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="txt" href="#E1:89_1_1_4_1_1_4"><i><font color="Green" title="E59">A6</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_4_1_1_5"><b>case </b></a><a NAME="E1:89_1_1_4_1_1_5"/><i><font color="Green" title="E59">A7</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c16">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</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="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</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="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</font> <a href="scmpds_1.html#K15" title="SCMPDS_1:func.15">P32const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K14" title="SCMPDS_1:func.14">P31address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</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="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_4"><i><font color="Green" title="E58">A5</font></i></a>, <a class="txt" href="#E1:89_1_1_4_1_1_5"><i><font color="Green" title="E59">A7</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</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="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</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="c9">c</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="c9">c</font> <a href="scmpds_1.html#K16" title="SCMPDS_1:func.16">P33const</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:89_1_1_4"/>
<span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5"><b>case </b></a><a NAME="E1:89_1_1_5"/>
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I3</font>,<span class="p3"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Olive" title="b2">d4</font>,<font color="Olive" title="b3">d5</font>,<font color="Olive" title="b4">k5</font>,<font color="Olive" title="b5">k6</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I3</font> is    <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, <font color="Olive" title="b2">d4</font>, <font color="Olive" title="b3">d5</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b4">k5</font>, <font color="Olive" title="b5">k6</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">I1</font> being    <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, <font color="Maroon" title="c13">d1</font>, <font color="Maroon" title="c14">d2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c15">k1</font>, <font color="Maroon" title="c16">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:89_1_1_5"/><i><font color="Green" title="E58">A8</font></i>: 
( <font color="Maroon" title="c9">c</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="c12">I1</font>,<span class="p2"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c15">k1</font>,<font color="Maroon" title="c16">k2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_1_1_5_1_1"/>
( <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 </span><b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1_1"><b>case </b></a><a NAME="E1:89_1_1_5_1_1_1"/><i><font color="Green" title="E59">A9</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c17">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</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="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="#E1:89_1_1_5_1_1_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</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="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1_2"><b>case </b></a><a NAME="E1:89_1_1_5_1_1_2"/><i><font color="Green" title="E59">A10</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c17">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="#E1:89_1_1_5_1_1_2"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1_3"><b>case </b></a><a NAME="E1:89_1_1_5_1_1_3"/><i><font color="Green" title="E59">A11</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c17">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="#E1:89_1_1_5_1_1_3"><i><font color="Green" title="E59">A11</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1_4"><b>case </b></a><a NAME="E1:89_1_1_5_1_1_4"/><i><font color="Green" title="E59">A12</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c17">SA</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c18">SB</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">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="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p0">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p0">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="#E1:89_1_1_5_1_1_4"><i><font color="Green" title="E59">A12</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p5">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T28" title="SCMPDS_1:th.28">SCMPDS_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
<br/>.= 
<font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_1_1_5_1_1_5"><b>case </b></a><a NAME="E1:89_1_1_5_1_1_5"/><i><font color="Green" title="E59">A13</font></i>: 
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c17">SS</font> =  <a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">S</font> <a href="scmpds_1.html#K6" title="SCMPDS_1:func.6">.</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> = 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K4" title="SCMPDS_1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">S</font>,<span class="p3">(<span class="default"><a href="scmpds_1.html#K7" title="SCMPDS_1:func.7">Address_Add</a> <font color="Maroon" title="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmpds_1.html#K3" title="SCMPDS_1:func.3">IC</a> <font color="Maroon" title="c10">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="txt" href="#E3:89_1_1_5"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="#E1:89_1_1_5_1_1_5"><i><font color="Green" title="E59">A13</font></i></a>, <a class="ref" href="scmpds_1.html#D24" title="SCMPDS_1:def.24">SCMPDS_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_1.html#K5" title="SCMPDS_1:func.5">SCM-Chg</a> <font color="Maroon" title="c10">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="c10">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K17" title="SCMPDS_1:func.17">P41address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K19" title="SCMPDS_1:func.19">P43const</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">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="c10">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K18" title="SCMPDS_1:func.18">P42address</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c9">c</font> <a href="scmpds_1.html#K20" title="SCMPDS_1:func.20">P44const</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</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="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
<b>by </b><i><a class="ref" href="scmpds_1.html#T32" title="SCMPDS_1:th.32">SCMPDS_1:32</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:89_1_1_5"/>
<span class="p1">(<span class="default"><a href="scmpds_1.html#K24" title="SCMPDS_1:func.24">SCM-Exec-Res</a> <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:89"/>
<font color="Maroon" title="c6">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">l</font>
 <b>by </b><i><a class="ref" href="scmpds_1.html#D25" title="SCMPDS_1:def.25">SCMPDS_1:def 25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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