<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</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">s</font>, <font color="Olive" title="b2">s1</font> being  <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> <br/> for <font color="Olive" title="b3">J</font> being <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Olive" title="b3">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font> holds <br/> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Olive" title="b1">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">s1</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">J</font> being <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Olive" title="b1">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font> holds <br/> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">J</font> be  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</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"> ( <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font> implies  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span> )</span><br/>







<b>set </b><font color="Maroon" title="c6">pJ</font> =  <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font>;<br/>
<b>set </b><font color="Maroon" title="c7">IsJ</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">s2</font> = <font color="Maroon" title="c4">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:57"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c9">i</font> =  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font>;<br/>
<b>set </b><font color="Maroon" title="c10">ss</font> = <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">k</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">Nl</font> =  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> as    <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>  ;<br/>
<i><font color="Green" title="E36">A4</font></i>:  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">Nl</font> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</a></i>
;<br/>
<a NAME="E5:57"/><i><font color="Green" title="E37">A5</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">IEn</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>;<br/>
<div><i><font color="Green" title="E38">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">d</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c14">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#T112" title="AMI_1:th.112">AMI_1:112</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>
<b>reconsider </b><font color="Maroon" title="c14">n1</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E8:57"/><i><font color="Green" title="E39">A7</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c14">n1</font>
 
;<br/>
<a NAME="E9:57"/><i><font color="Green" title="E40">A8</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s1</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E10:57"/><b>then </b><i><font color="Green" title="E41">A9</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:57"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="scmpds_4.html#D9" title="SCMPDS_4:def.9">SCMPDS_4:def 9</a></i>;<br/>
<a NAME="E11:57"/>
 <a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="#E1:57"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="#E9:57"><i><font color="Green" title="E40">A8</font></i></a>, <a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a>, <a class="ref" href="scmpds_4.html#T57" title="SCMPDS_4:th.57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E12:57"/><b>then </b>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c14">n1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E10:57"><i><font color="Green" title="E41">A9</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E13:57"/><b>then </b><i><font color="Green" title="E42">A10</font></i>: 
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp;  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="scmpds_4.html#R1" title="SCMPDS_4:pred.1">valid_at</a> <font color="Maroon" title="c14">n1</font> )
 
<b>by </b><i><a class="txt" href="#E10:57"><i><font color="Green" title="E41">A9</font></i></a>, <a class="ref" href="scmpds_4.html#D12" title="SCMPDS_4:def.12">SCMPDS_4:def 12</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 </span><b>by </b><i><a class="txt" href="#E13:57"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="nat_1.html#T38" title="NAT_1:th.38">NAT_1:38</a>, <a class="ref" href="scmpds_2.html#T15" title="SCMPDS_2:th.15">SCMPDS_2:15</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_1"><b>suppose </b></a><a NAME="E1:57_3_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_1"/><i><font color="Green" title="E43">A11</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <font color="Maroon" title="c15">k1</font> &amp; <font color="Maroon" title="c14">n1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c15">k1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E13:57"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_4.html#D11" title="SCMPDS_4:def.11">SCMPDS_4:def 11</a></i>;<br/><a NAME="E4:57_3_1"/><i><font color="Green" title="E44">A12</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c15">k1</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_1"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><i><font color="Green" title="E45">A13</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c15">k1</font>
<b>by </b><i><a class="txt" href="#E3:57_3_1"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="#E5:57"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="#E8:57"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="#E3:57_3_1"><i><font color="Green" title="E43">A11</font></i></a>, <a class="txt" href="#E4:57_3_1"><i><font color="Green" title="E44">A12</font></i></a>, <a class="ref" href="scmpds_4.html#T82" title="SCMPDS_4:th.82">SCMPDS_4:82</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c16">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_1"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_1"><i><font color="Green" title="E43">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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><b>hence </b><a NAME="E7:57_3_1"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_1"><i><font color="Green" title="E45">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_2"><b>suppose </b></a><a NAME="E1:57_3_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_2"/><i><font color="Green" title="E43">A14</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c16">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37" title="SCMPDS_2:th.37">SCMPDS_2:37</a></i>;<br/><a NAME="E4:57_3_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>;<br/><a NAME="E5:57_3_2"/><b>then </b><i><font color="Green" title="E44">A15</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_2_1_1"/>
( <font color="Maroon" title="c15">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font> or <font color="Maroon" title="c15">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_2_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_2_1_1_1"/><i><font color="Green" title="E45">A16</font></i>: 
<font color="Maroon" title="c15">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font> = 
<font color="Maroon" title="c16">k1</font>
<b>by </b><i><a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="txt" href="#E1:57_3_2_1_1_1"><i><font color="Green" title="E45">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_2_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_2_1_1_2"/><i><font color="Green" title="E45">A17</font></i>: 
<font color="Maroon" title="c15">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="txt" href="#E1:57_3_2_1_1_2"><i><font color="Green" title="E45">A17</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c17">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:57_3_2"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_2"><i><font color="Green" title="E44">A15</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_3"><b>suppose </b></a><a NAME="E1:57_3_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font>, <font color="Maroon" title="c17">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_3"/><i><font color="Green" title="E43">A18</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Maroon" title="c17">k2</font> &amp; <font color="Maroon" title="c14">n1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E13:57"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_4.html#D11" title="SCMPDS_4:def.11">SCMPDS_4:def 11</a></i>;<br/><div><i><font color="Green" title="E44">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_3_1_1"/>
( <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_3_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_3_1_1_1"/><i><font color="Green" title="E45">A20</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_3_1_1_1"/><b>then </b><i><font color="Green" title="E46">A21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_3_1_1_1"/><i><font color="Green" title="E47">A22</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c17">k2</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="#E1:57_3_3_1_1_1"><i><font color="Green" title="E45">A20</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>;<br/><b>thus </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="#E3:57_3_3_1_1_1"><i><font color="Green" title="E46">A21</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="#E5:57"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="#E8:57"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="#E4:57_3_3_1_1_1"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="scmpds_4.html#T82" title="SCMPDS_4:th.82">SCMPDS_4:82</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</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="57_3_3_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_3_1_1_2"/><i><font color="Green" title="E45">A23</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_3_1_1_2"/><b>then </b><i><font color="Green" title="E46">A24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_3_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="#E1:57_3_3_1_1_2"><i><font color="Green" title="E45">A23</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>;<br/><b>hence </b><a NAME="E5:57_3_3_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="#E3:57_3_3_1_1_2"><i><font color="Green" title="E46">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_3"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T67" title="SCMPDS_2:th.67">SCMPDS_2:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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><b>hence </b><a NAME="E6:57_3_3"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E4:57_3_3"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_4"><b>suppose </b></a><a NAME="E1:57_3_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font>, <font color="Maroon" title="c17">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_4"/><i><font color="Green" title="E43">A25</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c17">k2</font> &amp; <font color="Maroon" title="c14">n1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E13:57"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_4.html#D11" title="SCMPDS_4:def.11">SCMPDS_4:def 11</a></i>;<br/><div><i><font color="Green" title="E44">A26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_4_1_1"/>
( <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_4_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_4_1_1_1"/><i><font color="Green" title="E45">A27</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_4_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_4_1_1_1"/><b>then </b><i><font color="Green" title="E46">A28</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_4_1_1_1"/><i><font color="Green" title="E47">A29</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c17">k2</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="txt" href="#E1:57_3_4_1_1_1"><i><font color="Green" title="E45">A27</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/><b>thus </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="txt" href="#E3:57_3_4_1_1_1"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="#E5:57"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="#E8:57"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="txt" href="#E4:57_3_4_1_1_1"><i><font color="Green" title="E47">A29</font></i></a>, <a class="ref" href="scmpds_4.html#T82" title="SCMPDS_4:th.82">SCMPDS_4:82</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</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="57_3_4_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_4_1_1_2"/><i><font color="Green" title="E45">A30</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_4_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_4_1_1_2"/><b>then </b><i><font color="Green" title="E46">A31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_4_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="txt" href="#E1:57_3_4_1_1_2"><i><font color="Green" title="E45">A30</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/><b>hence </b><a NAME="E5:57_3_4_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="txt" href="#E3:57_3_4_1_1_2"><i><font color="Green" title="E46">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_4"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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><b>hence </b><a NAME="E6:57_3_4"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E4:57_3_4"><i><font color="Green" title="E44">A26</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_5"><b>suppose </b></a><a NAME="E1:57_3_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font>, <font color="Maroon" title="c17">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_5"/><i><font color="Green" title="E43">A32</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <font color="Maroon" title="c17">k2</font> &amp; <font color="Maroon" title="c14">n1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">k2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E13:57"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="scmpds_4.html#D11" title="SCMPDS_4:def.11">SCMPDS_4:def 11</a></i>;<br/><div><i><font color="Green" title="E44">A33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_5_1_1"/>
( <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_5_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_5_1_1_1"/><i><font color="Green" title="E45">A34</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_5_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_5_1_1_1"/><b>then </b><i><font color="Green" title="E46">A35</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_5_1_1_1"/><i><font color="Green" title="E47">A36</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c17">k2</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="txt" href="#E1:57_3_5_1_1_1"><i><font color="Green" title="E45">A34</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>;<br/><b>thus </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="txt" href="#E3:57_3_5_1_1_1"><i><font color="Green" title="E46">A35</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="#E5:57"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="#E8:57"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="txt" href="#E4:57_3_5_1_1_1"><i><font color="Green" title="E47">A36</font></i></a>, <a class="ref" href="scmpds_4.html#T82" title="SCMPDS_4:th.82">SCMPDS_4:82</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</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="57_3_5_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_5_1_1_2"/><i><font color="Green" title="E45">A37</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:57_3_5_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E3:57_3_5_1_1_2"/><b>then </b><i><font color="Green" title="E46">A38</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><a NAME="E4:57_3_5_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="txt" href="#E1:57_3_5_1_1_2"><i><font color="Green" title="E45">A37</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>;<br/><b>hence </b><a NAME="E5:57_3_5_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="txt" href="#E3:57_3_5_1_1_2"><i><font color="Green" title="E46">A38</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font></span><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_5"><i><font color="Green" title="E43">A32</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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><b>hence </b><a NAME="E6:57_3_5"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E4:57_3_5"><i><font color="Green" title="E44">A33</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_6"><b>suppose </b></a><a NAME="E1:57_3_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font>, <font color="Maroon" title="c17">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_6"/><i><font color="Green" title="E43">A39</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">k1</font> <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <font color="Maroon" title="c17">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42" title="SCMPDS_2:th.42">SCMPDS_2:42</a></i>;<br/><a NAME="E4:57_3_6"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>;<br/><a NAME="E5:57_3_6"/><b>then </b><i><font color="Green" title="E44">A40</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_6_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_6_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_6_1_1_1"/><i><font color="Green" title="E45">A41</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_6_1_1_1"/><b>then </b><i><font color="Green" title="E46">A42</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="txt" href="#E1:57_3_6_1_1_1"><i><font color="Green" title="E45">A41</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="txt" href="#E2:57_3_6_1_1_1"><i><font color="Green" title="E46">A42</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_6_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_6_1_1_2"/><i><font color="Green" title="E45">A43</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_6_1_1_2"/><b>then </b><i><font color="Green" title="E46">A44</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="txt" href="#E1:57_3_6_1_1_2"><i><font color="Green" title="E45">A43</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_6"><i><font color="Green" title="E43">A39</font></i></a>, <a class="txt" href="#E2:57_3_6_1_1_2"><i><font color="Green" title="E46">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_6"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_6"><i><font color="Green" title="E44">A40</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/><b>thus </b><a NAME="E8:57_3_6"/>
verum
 ; <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="57_3_7"><b>suppose </b></a><a NAME="E1:57_3_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c16">k1</font>, <font color="Maroon" title="c17">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_7"/><i><font color="Green" title="E43">A45</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c16">k1</font>,<font color="Maroon" title="c17">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43" title="SCMPDS_2:th.43">SCMPDS_2:43</a></i>;<br/><a NAME="E4:57_3_7"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>;<br/><a NAME="E5:57_3_7"/><b>then </b><i><font color="Green" title="E44">A46</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_7_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_7_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_7_1_1_1"/><i><font color="Green" title="E45">A47</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_7_1_1_1"/><b>then </b><i><font color="Green" title="E46">A48</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="txt" href="#E1:57_3_7_1_1_1"><i><font color="Green" title="E45">A47</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">k2</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="txt" href="#E2:57_3_7_1_1_1"><i><font color="Green" title="E46">A48</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_7_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_7_1_1_2"/><i><font color="Green" title="E45">A49</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_7_1_1_2"/><b>then </b><i><font color="Green" title="E46">A50</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c16">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">b</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="txt" href="#E1:57_3_7_1_1_2"><i><font color="Green" title="E45">A49</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="txt" href="#E3:57_3_7"><i><font color="Green" title="E43">A45</font></i></a>, <a class="txt" href="#E2:57_3_7_1_1_2"><i><font color="Green" title="E46">A50</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">b</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_7"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_7"><i><font color="Green" title="E44">A46</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_8"><b>suppose </b></a><a NAME="E1:57_3_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c16">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c17">k1</font>, <font color="Maroon" title="c18">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_8"/><i><font color="Green" title="E43">A51</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c17">k1</font>,<font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c18">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44" title="SCMPDS_2:th.44">SCMPDS_2:44</a></i>;<br/><a NAME="E4:57_3_8"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>;<br/><a NAME="E5:57_3_8"/><b>then </b><i><font color="Green" title="E44">A52</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_8_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_8_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_8_1_1_1"/><i><font color="Green" title="E45">A53</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_8_1_1_1"/><b>then </b><i><font color="Green" title="E46">A54</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><i><font color="Green" title="E47">A55</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="txt" href="#E1:57_3_8_1_1_1"><i><font color="Green" title="E45">A53</font></i></a>, <a class="txt" href="#E3:57_3_8_1_1_1"><i><font color="Green" title="E47">A55</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="txt" href="#E2:57_3_8_1_1_1"><i><font color="Green" title="E46">A54</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_8_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_8_1_1_2"/><i><font color="Green" title="E45">A56</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_8_1_1_2"/><b>then </b><i><font color="Green" title="E46">A57</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="txt" href="#E1:57_3_8_1_1_2"><i><font color="Green" title="E45">A56</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_8"><i><font color="Green" title="E43">A51</font></i></a>, <a class="txt" href="#E2:57_3_8_1_1_2"><i><font color="Green" title="E46">A57</font></i></a>, <a class="ref" href="scmpds_2.html#T61" title="SCMPDS_2:th.61">SCMPDS_2:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_8"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_8"><i><font color="Green" title="E44">A52</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_9"><b>suppose </b></a><a NAME="E1:57_3_9"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c16">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c17">k1</font>, <font color="Maroon" title="c18">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_9"/><i><font color="Green" title="E43">A58</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c17">k1</font>,<font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c18">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></i>;<br/><a NAME="E4:57_3_9"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>;<br/><a NAME="E5:57_3_9"/><b>then </b><i><font color="Green" title="E44">A59</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_9_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_9_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_9_1_1_1"/><i><font color="Green" title="E45">A60</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_9_1_1_1"/><b>then </b><i><font color="Green" title="E46">A61</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><i><font color="Green" title="E47">A62</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="txt" href="#E1:57_3_9_1_1_1"><i><font color="Green" title="E45">A60</font></i></a>, <a class="txt" href="#E3:57_3_9_1_1_1"><i><font color="Green" title="E47">A62</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="txt" href="#E2:57_3_9_1_1_1"><i><font color="Green" title="E46">A61</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_9_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_9_1_1_2"/><i><font color="Green" title="E45">A63</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_9_1_1_2"/><b>then </b><i><font color="Green" title="E46">A64</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="txt" href="#E1:57_3_9_1_1_2"><i><font color="Green" title="E45">A63</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_9"><i><font color="Green" title="E43">A58</font></i></a>, <a class="txt" href="#E2:57_3_9_1_1_2"><i><font color="Green" title="E46">A64</font></i></a>, <a class="ref" href="scmpds_2.html#T62" title="SCMPDS_2:th.62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_9"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_9"><i><font color="Green" title="E44">A59</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_10"><b>suppose </b></a><a NAME="E1:57_3_10"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c16">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c17">k1</font>, <font color="Maroon" title="c18">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_10"/><i><font color="Green" title="E43">A65</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K15" title="SCMPDS_2:func.15">MultBy</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c17">k1</font>,<font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c18">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></i>;<br/><a NAME="E4:57_3_10"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>;<br/><a NAME="E5:57_3_10"/><b>then </b><i><font color="Green" title="E44">A66</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_10_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_10_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_10_1_1_1"/><i><font color="Green" title="E45">A67</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_10_1_1_1"/><b>then </b><i><font color="Green" title="E46">A68</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><i><font color="Green" title="E47">A69</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="txt" href="#E1:57_3_10_1_1_1"><i><font color="Green" title="E45">A67</font></i></a>, <a class="txt" href="#E3:57_3_10_1_1_1"><i><font color="Green" title="E47">A69</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="txt" href="#E2:57_3_10_1_1_1"><i><font color="Green" title="E46">A68</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_10_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_10_1_1_2"/><i><font color="Green" title="E45">A70</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_10_1_1_2"/><b>then </b><i><font color="Green" title="E46">A71</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="txt" href="#E1:57_3_10_1_1_2"><i><font color="Green" title="E45">A70</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_10"><i><font color="Green" title="E43">A65</font></i></a>, <a class="txt" href="#E2:57_3_10_1_1_2"><i><font color="Green" title="E46">A71</font></i></a>, <a class="ref" href="scmpds_2.html#T63" title="SCMPDS_2:th.63">SCMPDS_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_10"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_10"><i><font color="Green" title="E44">A66</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_11"><b>suppose </b></a><a NAME="E1:57_3_11"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c16">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c17">k1</font>, <font color="Maroon" title="c18">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_11"/><i><font color="Green" title="E43">A72</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c17">k1</font>,<font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c18">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47" title="SCMPDS_2:th.47">SCMPDS_2:47</a></i>;<br/><a NAME="E4:57_3_11"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>;<br/><a NAME="E5:57_3_11"/><b>then </b><i><font color="Green" title="E44">A73</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><i><font color="Green" title="E45">A74</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><i><font color="Green" title="E46">A75</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span> = 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_11_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_11_1_3"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_11_1_3_1"><b>suppose </b></a><a NAME="E1:57_3_11_1_3_1"/><i><font color="Green" title="E47">A76</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_11_1_3_1"/><b>then </b><i><font color="Green" title="E48">A77</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E1:57_3_11_1"><i><font color="Green" title="E45">A74</font></i></a>, <a class="txt" href="#E2:57_3_11_1"><i><font color="Green" title="E46">A75</font></i></a>, <a class="txt" href="#E1:57_3_11_1_3_1"><i><font color="Green" title="E47">A76</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E2:57_3_11_1_3_1"><i><font color="Green" title="E48">A77</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_11_1_3_2"><b>suppose </b></a><a NAME="E1:57_3_11_1_3_2"/><i><font color="Green" title="E47">A78</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_11_1_3_2"/><b>then </b><i><font color="Green" title="E48">A79</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_11_1_3_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_11_1_3_2_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_11_1_3_2_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_11_1_3_2_1_1_1"/><i><font color="Green" title="E49">A80</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font></span><br/><div class="add"><a NAME="E2:57_3_11_1_3_2_1_1_1"/><b>then </b><i><font color="Green" title="E50">A81</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E1:57_3_11_1_3_2"><i><font color="Green" title="E47">A78</font></i></a>, <a class="txt" href="#E1:57_3_11_1_3_2_1_1_1"><i><font color="Green" title="E49">A80</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E2:57_3_11_1_3_2"><i><font color="Green" title="E48">A79</font></i></a>, <a class="txt" href="#E2:57_3_11_1_3_2_1_1_1"><i><font color="Green" title="E50">A81</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_11_1_3_2_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_11_1_3_2_1_1_2"/><i><font color="Green" title="E49">A82</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font></span><br/><div class="add"><a NAME="E2:57_3_11_1_3_2_1_1_2"/><b>then </b><i><font color="Green" title="E50">A83</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font></span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E1:57_3_11_1"><i><font color="Green" title="E45">A74</font></i></a>, <a class="txt" href="#E2:57_3_11_1"><i><font color="Green" title="E46">A75</font></i></a>, <a class="txt" href="#E1:57_3_11_1_3_2"><i><font color="Green" title="E47">A78</font></i></a>, <a class="txt" href="#E1:57_3_11_1_3_2_1_1_2"><i><font color="Green" title="E49">A82</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_11"><i><font color="Green" title="E43">A72</font></i></a>, <a class="txt" href="#E2:57_3_11_1_3_2"><i><font color="Green" title="E48">A79</font></i></a>, <a class="txt" href="#E2:57_3_11_1_3_2_1_1_2"><i><font color="Green" title="E50">A83</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:57_3_11"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_11"><i><font color="Green" title="E44">A73</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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="57_3_12"><b>suppose </b></a><a NAME="E1:57_3_12"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span> <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">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c15">a</font>, <font color="Maroon" title="c16">b</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> , <font color="Maroon" title="c17">k1</font>, <font color="Maroon" title="c18">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:57_3_12"/><i><font color="Green" title="E43">A84</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">a</font>,<font color="Maroon" title="c17">k1</font> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <font color="Maroon" title="c16">b</font>,<font color="Maroon" title="c18">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48" title="SCMPDS_2:th.48">SCMPDS_2:48</a></i>;<br/><a NAME="E4:57_3_12"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Nl</font>
 <b>by </b><i><a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/><a NAME="E5:57_3_12"/><b>then </b><i><font color="Green" title="E44">A85</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:57"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">c</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_3_12_1_1"/>
(  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font> or  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_3_12_1_1_1"><b>suppose </b></a><a NAME="E1:57_3_12_1_1_1"/><i><font color="Green" title="E45">A86</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_12_1_1_1"/><b>then </b><i><font color="Green" title="E46">A87</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="txt" href="#E1:57_3_12_1_1_1"><i><font color="Green" title="E45">A86</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c16">b</font></span>)</span>,<font color="Maroon" title="c18">k2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="txt" href="#E2:57_3_12_1_1_1"><i><font color="Green" title="E46">A87</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="57_3_12_1_1_2"><b>suppose </b></a><a NAME="E1:57_3_12_1_1_2"/><i><font color="Green" title="E45">A88</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 ; <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> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:57_3_12_1_1_2"/><b>then </b><i><font color="Green" title="E46">A89</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c15">a</font></span>)</span>,<font color="Maroon" title="c17">k1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="txt" href="#E1:57_3_12_1_1_2"><i><font color="Green" title="E45">A88</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="txt" href="#E3:57_3_12"><i><font color="Green" title="E43">A84</font></i></a>, <a class="txt" href="#E2:57_3_12_1_1_2"><i><font color="Green" title="E46">A89</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c19">c</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#T14" title="SCMPDS_3:th.14">SCMPDS_3:14</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="E7:57_3_12"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:57"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="#E5:57_3_12"><i><font color="Green" title="E44">A85</font></i></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</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>
