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

<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c2">s2</font> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s2</font> holds <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> <font color="Olive" title="b2">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Olive" title="b1">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c2">s2</font> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s2</font> holds <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> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c4">i</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c2">s2</font> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s2</font> implies ( <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> ) )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E15">A1</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c2">s2</font>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E16">A2</font></i>: 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c2">s2</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#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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c5">D</font> = <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">k1</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E4:31"/><i><font color="Green" title="E17">A4</font></i>: 
<span class="p1">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">s2</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font>
<b>by </b><i><a class="ref" href="nat_1.html#T39" title="NAT_1:th.39">NAT_1:39</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

<br/>.= 
 <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="c2">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="nat_1.html#T39" title="NAT_1:th.39">NAT_1:39</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><i><font color="Green" title="E18">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:31_2"/><i><font color="Green" title="E19">A6</font></i>: 
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 6 or 8 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> )
 <b>and </b><br/><a NAME="E2:31_2"/><i><font color="Green" title="E20">A7</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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"> <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><b>set </b><font color="Maroon" title="c7">I</font> =  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font>;<br/><a NAME="E3:31_2"/><i><font color="Green" title="E21">A8</font></i>: 
not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,6,7,8</span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:31_2_1"/><i><font color="Green" title="E22">A9</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,6,7,8</span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_2_1_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="#E1:31_2_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_1_1_1"><b>suppose </b></a><a NAME="E1:31_2_1_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:31_2"><i><font color="Green" title="E20">A7</font></i></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="31_2_1_1_2"><b>suppose </b></a><a NAME="E1:31_2_1_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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="31_2_1_1_3"><b>suppose </b></a><a NAME="E1:31_2_1_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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="31_2_1_1_4"><b>suppose </b></a><a NAME="E1:31_2_1_1_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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><a NAME="E4:31_2"/>
not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">6,7,8</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:31_2_2"/><i><font color="Green" title="E22">A10</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">6,7,8</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_2_2_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="#E1:31_2_2"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_2_1_1"><b>suppose </b></a><a NAME="E1:31_2_2_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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="31_2_2_1_2"><b>suppose </b></a><a NAME="E1:31_2_2_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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="31_2_2_1_3"><b>suppose </b></a><a NAME="E1:31_2_2_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div class="add"><b>hence </b><a NAME="E2:31_2_2_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:31_2"><i><font color="Green" title="E19">A6</font></i></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><a NAME="E5:31_2"/><b>then </b><i><font color="Green" title="E22">A11</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#D3" title="SCMFSA_4:def.3">SCMFSA_4:def 3</a></i>;<br/><a NAME="E6:31_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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_2"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="scmfsa6a.html#T23" target="_self" title="SCMFSA6A:th.23">Th23</a></i>;<br/><b>hence </b><a NAME="E7:31_2"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E3:31_2"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="#E5:31_2"><i><font color="Green" title="E22">A11</font></i></a>, <a class="ref" href="scmfsa6a.html#T23" target="_self" title="SCMFSA6A:th.23">Th23</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>
<a NAME="E6:31"/><i><font color="Green" title="E19">A12</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 11 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T35" title="SCMFSA_2:th.35">SCMFSA_2:35</a></i>;<br/>
<a NAME="E7:31"/><i><font color="Green" title="E20">A13</font></i>: 
(  not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/>
<a NAME="E8:31"/><i><font color="Green" title="E21">A14</font></i>: 
(  not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 9 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <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> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="#E6:31"><i><font color="Green" title="E19">A12</font></i></a>, <a class="txt" href="#E7:31"><i><font color="Green" title="E20">A13</font></i></a>, <a class="txt" href="#E8:31"><i><font color="Green" title="E21">A14</font></i></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a>, <a class="ref" href="nat_1.html#T33" title="NAT_1:th.33">NAT_1:33</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_1"><b>suppose </b></a><a NAME="E1:31_3_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <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"> ( <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:31_3_1"/><b>then </b><i><font color="Green" title="E22">A15</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122" title="SCMFSA_2:th.122">SCMFSA_2:122</a></i>;<br/><a NAME="E3:31_3_1"/><b>then </b>
(  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s1</font> &amp;  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:31_3_1"/>
( <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E2:31_3_1"><i><font color="Green" title="E22">A15</font></i></a>, <a class="ref" href="scmfsa_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</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="31_3_2"><b>suppose </b></a><a NAME="E1:31_3_2"/><i><font color="Green" title="E22">A16</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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#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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_2"/><i><font color="Green" title="E23">A17</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">:=</a> <font color="Maroon" title="c8">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54" title="SCMFSA_2:th.54">SCMFSA_2:54</a></i>;<br/><a NAME="E4:31_3_2"/><i><font color="Green" title="E24">A18</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="scmfsa_4.html#T9" title="SCMFSA_4:th.9">SCMFSA_4:9</a></i>;<br/><b>thus </b><a NAME="E5:31_3_2"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_2"><i><font color="Green" title="E22">A16</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_2_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> or <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_2_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_2_1_1_1"/><i><font color="Green" title="E26">A20</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="txt" href="#E4:31_3_2"><i><font color="Green" title="E24">A18</font></i></a>, <a class="txt" href="#E1:31_3_2_1_1_1"><i><font color="Green" title="E26">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</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="31_3_2_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_2_1_1_2"/><i><font color="Green" title="E26">A21</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="txt" href="#E4:31_3_2"><i><font color="Green" title="E24">A18</font></i></a>, <a class="txt" href="#E1:31_3_2_1_1_2"><i><font color="Green" title="E26">A21</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_2"><i><font color="Green" title="E23">A17</font></i></a>, <a class="txt" href="#E4:31_3_2"><i><font color="Green" title="E24">A18</font></i></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</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="E8:31_3_2"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_2"><i><font color="Green" title="E25">A19</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_3"><b>suppose </b></a><a NAME="E1:31_3_3"/><i><font color="Green" title="E22">A22</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_3"/><i><font color="Green" title="E23">A23</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">AddTo</a> <font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55" title="SCMFSA_2:th.55">SCMFSA_2:55</a></i>;<br/><a NAME="E4:31_3_3"/><i><font color="Green" title="E24">A24</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="ref" href="scmfsa_4.html#T10" title="SCMFSA_4:th.10">SCMFSA_4:10</a></i>;<br/><b>thus </b><a NAME="E5:31_3_3"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_3"><i><font color="Green" title="E22">A22</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_3_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> or <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_3_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_3_1_1_1"/><i><font color="Green" title="E26">A26</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:31_3_3_1_1_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="#E1:31_3_3_1_1_1"><i><font color="Green" title="E26">A26</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="#E4:31_3_3"><i><font color="Green" title="E24">A24</font></i></a>, <a class="txt" href="#E1:31_3_3_1_1_1"><i><font color="Green" title="E26">A26</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</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="31_3_3_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_3_1_1_2"/><i><font color="Green" title="E26">A27</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="#E4:31_3_3"><i><font color="Green" title="E24">A24</font></i></a>, <a class="txt" href="#E1:31_3_3_1_1_2"><i><font color="Green" title="E26">A27</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_3"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="#E4:31_3_3"><i><font color="Green" title="E24">A24</font></i></a>, <a class="ref" href="scmfsa_2.html#T90" title="SCMFSA_2:th.90">SCMFSA_2:90</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="E8:31_3_3"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_3"><i><font color="Green" title="E25">A25</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_4"><b>suppose </b></a><a NAME="E1:31_3_4"/><i><font color="Green" title="E22">A28</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_4"/><i><font color="Green" title="E23">A29</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">SubFrom</a> <font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56" title="SCMFSA_2:th.56">SCMFSA_2:56</a></i>;<br/><a NAME="E4:31_3_4"/><i><font color="Green" title="E24">A30</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="ref" href="scmfsa_4.html#T11" title="SCMFSA_4:th.11">SCMFSA_4:11</a></i>;<br/><b>thus </b><a NAME="E5:31_3_4"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_4"><i><font color="Green" title="E22">A28</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_4_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> or <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_4_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_4_1_1_1"/><i><font color="Green" title="E26">A32</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:31_3_4_1_1_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="txt" href="#E1:31_3_4_1_1_1"><i><font color="Green" title="E26">A32</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="txt" href="#E4:31_3_4"><i><font color="Green" title="E24">A30</font></i></a>, <a class="txt" href="#E1:31_3_4_1_1_1"><i><font color="Green" title="E26">A32</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</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="31_3_4_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_4_1_1_2"/><i><font color="Green" title="E26">A33</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="txt" href="#E4:31_3_4"><i><font color="Green" title="E24">A30</font></i></a>, <a class="txt" href="#E1:31_3_4_1_1_2"><i><font color="Green" title="E26">A33</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_4"><i><font color="Green" title="E23">A29</font></i></a>, <a class="txt" href="#E4:31_3_4"><i><font color="Green" title="E24">A30</font></i></a>, <a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</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="E8:31_3_4"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_4"><i><font color="Green" title="E25">A31</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_5"><b>suppose </b></a><a NAME="E1:31_3_5"/><i><font color="Green" title="E22">A34</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_5"/><i><font color="Green" title="E23">A35</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">MultBy</a> <font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57" title="SCMFSA_2:th.57">SCMFSA_2:57</a></i>;<br/><b>thus </b><a NAME="E4:31_3_5"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_5"><i><font color="Green" title="E22">A34</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><a NAME="E5:31_3_5"/><i><font color="Green" title="E24">A36</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="ref" href="scmfsa_4.html#T12" title="SCMFSA_4:th.12">SCMFSA_4:12</a></i>;<br/><div><i><font color="Green" title="E25">A37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_5_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> or <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_5_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_5_1_1_1"/><i><font color="Green" title="E26">A38</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:31_3_5_1_1_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="txt" href="#E1:31_3_5_1_1_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="txt" href="#E5:31_3_5"><i><font color="Green" title="E24">A36</font></i></a>, <a class="txt" href="#E1:31_3_5_1_1_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</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="31_3_5_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_5_1_1_2"/><i><font color="Green" title="E26">A39</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="txt" href="#E5:31_3_5"><i><font color="Green" title="E24">A36</font></i></a>, <a class="txt" href="#E1:31_3_5_1_1_2"><i><font color="Green" title="E26">A39</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_5"><i><font color="Green" title="E23">A35</font></i></a>, <a class="txt" href="#E5:31_3_5"><i><font color="Green" title="E24">A36</font></i></a>, <a class="ref" href="scmfsa_2.html#T92" title="SCMFSA_2:th.92">SCMFSA_2:92</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="E8:31_3_5"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_5"><i><font color="Green" title="E25">A37</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_6"><b>suppose </b></a><a NAME="E1:31_3_6"/><i><font color="Green" title="E22">A40</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font>, <font color="Maroon" title="c8">db</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_6"/><i><font color="Green" title="E23">A41</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">Divide</a> <font color="Maroon" title="c7">da</font>,<font color="Maroon" title="c8">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58" title="SCMFSA_2:th.58">SCMFSA_2:58</a></i>;<br/><a NAME="E4:31_3_6"/><i><font color="Green" title="E24">A42</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="ref" href="scmfsa_4.html#T13" title="SCMFSA_4:th.13">SCMFSA_4:13</a></i>;<br/><b>thus </b><a NAME="E5:31_3_6"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_6"><i><font color="Green" title="E22">A40</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A43</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_6_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">db</font> or ( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">db</font> ) or ( <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">db</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_6_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_6_1_1_1"/><i><font color="Green" title="E26">A44</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">db</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:31_3_6_1_1_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></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="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E1:31_3_6_1_1_1"><i><font color="Green" title="E26">A44</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E4:31_3_6"><i><font color="Green" title="E24">A42</font></i></a>, <a class="txt" href="#E1:31_3_6_1_1_1"><i><font color="Green" title="E26">A44</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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="31_3_6_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_6_1_1_2"/><i><font color="Green" title="E26">A45</font></i>: 
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">db</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:31_3_6_1_1_2"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></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="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">db</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E1:31_3_6_1_1_2"><i><font color="Green" title="E26">A45</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E4:31_3_6"><i><font color="Green" title="E24">A42</font></i></a>, <a class="txt" href="#E1:31_3_6_1_1_2"><i><font color="Green" title="E26">A45</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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="31_3_6_1_1_3"><b>suppose </b></a><a NAME="E1:31_3_6_1_1_3"/><i><font color="Green" title="E26">A46</font></i>: 
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> &amp; <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">db</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E4:31_3_6"><i><font color="Green" title="E24">A42</font></i></a>, <a class="txt" href="#E1:31_3_6_1_1_3"><i><font color="Green" title="E26">A46</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_6"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E4:31_3_6"><i><font color="Green" title="E24">A42</font></i></a>, <a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</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="E8:31_3_6"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_6"><i><font color="Green" title="E25">A43</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_7"><b>suppose </b></a><a NAME="E1:31_3_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">loc</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:31_3_7"/><i><font color="Green" title="E22">A47</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59" title="SCMFSA_2:th.59">SCMFSA_2:59</a></i>;<br/><a NAME="E4:31_3_7"/><i><font color="Green" title="E23">A48</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_3_7"><i><font color="Green" title="E22">A47</font></i></a>, <a class="ref" href="scmfsa_4.html#T14" title="SCMFSA_4:th.14">SCMFSA_4:14</a></i>;<br/><a NAME="E5:31_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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_7"><i><font color="Green" title="E22">A47</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>;<br/><b>hence </b><a NAME="E6:31_3_7"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31_3_7"><i><font color="Green" title="E23">A48</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E24">A49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_7"><i><font color="Green" title="E22">A47</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="#E4:31_3_7"><i><font color="Green" title="E23">A48</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</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="hs2(this)" href="javascript:()" title="31_3_7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_7"><i><font color="Green" title="E22">A47</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="#E4:31_3_7"><i><font color="Green" title="E23">A48</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</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="E9:31_3_7"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:31_3_7"><i><font color="Green" title="E24">A49</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_8"><b>suppose </b></a><a NAME="E1:31_3_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">loc</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c8">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_8"/><i><font color="Green" title="E22">A50</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:31_3_8"/><i><font color="Green" title="E23">A51</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_3_8"><i><font color="Green" title="E22">A50</font></i></a>, <a class="ref" href="scmfsa_4.html#T15" title="SCMFSA_4:th.15">SCMFSA_4:15</a></i>;<br/><div><i><font color="Green" title="E24">A52</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_8"><i><font color="Green" title="E22">A50</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E4:31_3_8"><i><font color="Green" title="E23">A51</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</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><i><font color="Green" title="E25">A53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_8_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_8"><i><font color="Green" title="E22">A50</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E4:31_3_8"><i><font color="Green" title="E23">A51</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</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>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_8_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3_8_3_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&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="31_3_8_3_1_1"><b>suppose </b></a><a NAME="E1:31_3_8_3_1_1"/><i><font color="Green" title="E26">A54</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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"> <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_3_8_3_1_1"/><b>then </b><i><font color="Green" title="E27">A55</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><a NAME="E3:31_3_8_3_1_1"/>
 <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_8"><i><font color="Green" title="E22">A50</font></i></a>, <a class="txt" href="#E1:31_3_8_3_1_1"><i><font color="Green" title="E26">A54</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>;<br/><b>hence </b><a NAME="E4:31_3_8_3_1_1"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31_3_8"><i><font color="Green" title="E23">A51</font></i></a>, <a class="txt" href="#E2:31_3_8_3_1_1"><i><font color="Green" title="E27">A55</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</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="31_3_8_3_1_2"><b>suppose </b></a><a NAME="E1:31_3_8_3_1_2"/><i><font color="Green" title="E26">A56</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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"> <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_3_8_3_1_2"/><b>then </b><i><font color="Green" title="E27">A57</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><a NAME="E3:31_3_8_3_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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_3_8"><i><font color="Green" title="E22">A50</font></i></a>, <a class="txt" href="#E1:31_3_8_3_1_2"><i><font color="Green" title="E26">A56</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>;<br/><b>hence </b><a NAME="E4:31_3_8_3_1_2"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E4:31_3_8"><i><font color="Green" title="E23">A51</font></i></a>, <a class="txt" href="#E2:31_3_8_3_1_2"><i><font color="Green" title="E27">A57</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</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>thus </b><a NAME="E8:31_3_8"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31_3_8"><i><font color="Green" title="E24">A52</font></i></a>, <a class="txt" href="#E6:31_3_8"><i><font color="Green" title="E25">A53</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_9"><b>suppose </b></a><a NAME="E1:31_3_9"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">loc</font> being    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c8">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:31_3_9"/><i><font color="Green" title="E22">A58</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:31_3_9"/><i><font color="Green" title="E23">A59</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">loc</font> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_3_9"><i><font color="Green" title="E22">A58</font></i></a>, <a class="ref" href="scmfsa_4.html#T16" title="SCMFSA_4:th.16">SCMFSA_4:16</a></i>;<br/><div><i><font color="Green" title="E24">A60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_9"><i><font color="Green" title="E22">A58</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E4:31_3_9"><i><font color="Green" title="E23">A59</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</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><i><font color="Green" title="E25">A61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_9_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_9"><i><font color="Green" title="E22">A58</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E4:31_3_9"><i><font color="Green" title="E23">A59</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</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>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_9_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3_9_3_1"/>
( <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="31_3_9_3_1_1"><b>suppose </b></a><a NAME="E1:31_3_9_3_1_1"/><i><font color="Green" title="E26">A62</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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"> <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_3_9_3_1_1"/><b>then </b><i><font color="Green" title="E27">A63</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><a NAME="E3:31_3_9_3_1_1"/>
 <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">loc</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_9"><i><font color="Green" title="E22">A58</font></i></a>, <a class="txt" href="#E1:31_3_9_3_1_1"><i><font color="Green" title="E26">A62</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>;<br/><b>hence </b><a NAME="E4:31_3_9_3_1_1"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31_3_9"><i><font color="Green" title="E23">A59</font></i></a>, <a class="txt" href="#E2:31_3_9_3_1_1"><i><font color="Green" title="E27">A63</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</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="31_3_9_3_1_2"><b>suppose </b></a><a NAME="E1:31_3_9_3_1_2"/><i><font color="Green" title="E26">A64</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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"> <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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div class="add"><a NAME="E2:31_3_9_3_1_2"/><b>then </b><i><font color="Green" title="E27">A65</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <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="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><a NAME="E3:31_3_9_3_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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:31_3_9"><i><font color="Green" title="E22">A58</font></i></a>, <a class="txt" href="#E1:31_3_9_3_1_2"><i><font color="Green" title="E26">A64</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>;<br/><b>hence </b><a NAME="E4:31_3_9_3_1_2"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:31"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E4:31_3_9"><i><font color="Green" title="E23">A59</font></i></a>, <a class="txt" href="#E2:31_3_9_3_1_2"><i><font color="Green" title="E27">A65</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</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>thus </b><a NAME="E8:31_3_9"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31_3_9"><i><font color="Green" title="E24">A60</font></i></a>, <a class="txt" href="#E6:31_3_9"><i><font color="Green" title="E25">A61</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_10"><b>suppose </b></a><a NAME="E1:31_3_10"/><i><font color="Green" title="E22">A66</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">db</font>, <font color="Maroon" title="c8">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:31_3_10"/><i><font color="Green" title="E23">A67</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62" title="SCMFSA_2:th.62">SCMFSA_2:62</a></i>;<br/><a NAME="E4:31_3_10"/><i><font color="Green" title="E24">A68</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="ref" href="scmfsa_4.html#T17" title="SCMFSA_4:th.17">SCMFSA_4:17</a></i>;<br/><b>thus </b><a NAME="E5:31_3_10"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_10"><i><font color="Green" title="E22">A66</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A69</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_10_1_1"/>
( <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</font> or <font color="Maroon" title="c10">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_10_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_10_1_1_1"/><i><font color="Green" title="E26">A70</font></i>: 
<font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c11">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:31_3_10_1_1_1"/><i><font color="Green" title="E27">A71</font></i>: 
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
 <b>and </b><br/><a NAME="E4:31_3_10_1_1_1"/><i><font color="Green" title="E28">A72</font></i>: 
<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"><font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font></span>)</span>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">m</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">m2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:31_3_10_1_1_1"/><i><font color="Green" title="E29">A73</font></i>: 
<font color="Maroon" title="c12">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
 <b>and </b><br/><a NAME="E7:31_3_10_1_1_1"/><i><font color="Green" title="E30">A74</font></i>: 
<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"><font color="Maroon" title="c8">da</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m2</font>
 <b>by </b><i><a class="txt" href="#E1:31_3_10_1_1_1"><i><font color="Green" title="E26">A70</font></i></a>, <a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</a></i>;<br/><a NAME="E8:31_3_10_1_1_1"/>
( <font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">m2</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E3:31_3_10_1_1_1"><i><font color="Green" title="E27">A71</font></i></a>, <a class="txt" href="#E6:31_3_10_1_1_1"><i><font color="Green" title="E29">A73</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><b>hence </b><a NAME="E9:31_3_10_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="txt" href="#E4:31_3_10_1_1_1"><i><font color="Green" title="E28">A72</font></i></a>, <a class="txt" href="#E7:31_3_10_1_1_1"><i><font color="Green" title="E30">A74</font></i></a>, <a class="ref" href="scmfsa_4.html#T17" title="SCMFSA_4:th.17">SCMFSA_4:17</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="31_3_10_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_10_1_1_2"/><i><font color="Green" title="E26">A75</font></i>: 
<font color="Maroon" title="c10">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="txt" href="#E4:31_3_10"><i><font color="Green" title="E24">A68</font></i></a>, <a class="txt" href="#E1:31_3_10_1_1_2"><i><font color="Green" title="E26">A75</font></i></a>, <a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_10"><i><font color="Green" title="E23">A67</font></i></a>, <a class="txt" href="#E4:31_3_10"><i><font color="Green" title="E24">A68</font></i></a>, <a class="ref" href="scmfsa_2.html#T98" title="SCMFSA_2:th.98">SCMFSA_2:98</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="E8:31_3_10"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_10"><i><font color="Green" title="E25">A69</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_11"><b>suppose </b></a><a NAME="E1:31_3_11"/><i><font color="Green" title="E22">A76</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">db</font>, <font color="Maroon" title="c8">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:31_3_11"/><i><font color="Green" title="E23">A77</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c8">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63" title="SCMFSA_2:th.63">SCMFSA_2:63</a></i>;<br/><a NAME="E4:31_3_11"/><i><font color="Green" title="E24">A78</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="ref" href="scmfsa_4.html#T18" title="SCMFSA_4:th.18">SCMFSA_4:18</a></i>;<br/><b>thus </b><a NAME="E5:31_3_11"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_11"><i><font color="Green" title="E22">A76</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A79</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="txt" href="#E4:31_3_11"><i><font color="Green" title="E24">A78</font></i></a>, <a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</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="hs2(this)" href="javascript:()" title="31_3_11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">g</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_11_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3_11_2_1"/>
( <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> or <font color="Maroon" title="c10">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_11_2_1_1"><b>suppose </b></a><a NAME="E1:31_3_11_2_1_1"/><i><font color="Green" title="E26">A80</font></i>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c11">m1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:31_3_11_2_1_1"/><i><font color="Green" title="E27">A81</font></i>: 
<font color="Maroon" title="c11">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
 <b>and </b><br/><a NAME="E4:31_3_11_2_1_1"/><i><font color="Green" title="E28">A82</font></i>: 
<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"><font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c8">da</font></span>)</span>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c11">m1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">m2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:31_3_11_2_1_1"/><i><font color="Green" title="E29">A83</font></i>: 
<font color="Maroon" title="c12">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">db</font></span>)</span>
 <b>and </b><br/><a NAME="E7:31_3_11_2_1_1"/><i><font color="Green" title="E30">A84</font></i>: 
<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"><font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">db</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c8">da</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c12">m2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</a></i>;<br/><a NAME="E8:31_3_11_2_1_1"/>
( <font color="Maroon" title="c11">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">m2</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c8">da</font> &amp; <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> )
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E3:31_3_11_2_1_1"><i><font color="Green" title="E27">A81</font></i></a>, <a class="txt" href="#E6:31_3_11_2_1_1"><i><font color="Green" title="E29">A83</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</a></i>;<br/><b>hence </b><a NAME="E9:31_3_11_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="txt" href="#E1:31_3_11_2_1_1"><i><font color="Green" title="E26">A80</font></i></a>, <a class="txt" href="#E4:31_3_11_2_1_1"><i><font color="Green" title="E28">A82</font></i></a>, <a class="txt" href="#E7:31_3_11_2_1_1"><i><font color="Green" title="E30">A84</font></i></a>, <a class="ref" href="scmfsa_4.html#T18" title="SCMFSA_4:th.18">SCMFSA_4:18</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="31_3_11_2_1_2"><b>suppose </b></a><a NAME="E1:31_3_11_2_1_2"/><i><font color="Green" title="E26">A85</font></i>: 
<font color="Maroon" title="c10">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font>
<b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c10">g</font>
<b>by </b><i><a class="txt" href="#E3:31_3_11"><i><font color="Green" title="E23">A77</font></i></a>, <a class="txt" href="#E4:31_3_11"><i><font color="Green" title="E24">A78</font></i></a>, <a class="txt" href="#E1:31_3_11_2_1_2"><i><font color="Green" title="E26">A85</font></i></a>, <a class="ref" href="scmfsa_2.html#T99" title="SCMFSA_2:th.99">SCMFSA_2:99</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="E8:31_3_11"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_11"><i><font color="Green" title="E25">A79</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_12"><b>suppose </b></a><a NAME="E1:31_3_12"/><i><font color="Green" title="E22">A86</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:31_3_12"/><i><font color="Green" title="E23">A87</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=len</a> <font color="Maroon" title="c8">f</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64" title="SCMFSA_2:th.64">SCMFSA_2:64</a></i>;<br/><a NAME="E4:31_3_12"/><i><font color="Green" title="E24">A88</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="ref" href="scmfsa_4.html#T19" title="SCMFSA_4:th.19">SCMFSA_4:19</a></i>;<br/><b>thus </b><a NAME="E5:31_3_12"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_12"><i><font color="Green" title="E22">A86</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A89</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_3_12_1_1"/>
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</font> or <font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_12_1_1_1"><b>suppose </b></a><a NAME="E1:31_3_12_1_1_1"/><i><font color="Green" title="E26">A90</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="txt" href="#E4:31_3_12"><i><font color="Green" title="E24">A88</font></i></a>, <a class="txt" href="#E1:31_3_12_1_1_1"><i><font color="Green" title="E26">A90</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</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="31_3_12_1_1_2"><b>suppose </b></a><a NAME="E1:31_3_12_1_1_2"/><i><font color="Green" title="E26">A91</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">da</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="txt" href="#E4:31_3_12"><i><font color="Green" title="E24">A88</font></i></a>, <a class="txt" href="#E1:31_3_12_1_1_2"><i><font color="Green" title="E26">A91</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="txt" href="#E3:31_3_12"><i><font color="Green" title="E23">A87</font></i></a>, <a class="txt" href="#E4:31_3_12"><i><font color="Green" title="E24">A88</font></i></a>, <a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</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="E8:31_3_12"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_12"><i><font color="Green" title="E25">A89</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_13"><b>suppose </b></a><a NAME="E1:31_3_13"/><i><font color="Green" title="E22">A92</font></i>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> &amp;  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">da</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:31_3_13"/><i><font color="Green" title="E23">A93</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c7">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></i>;<br/><a NAME="E4:31_3_13"/><i><font color="Green" title="E24">A94</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="ref" href="scmfsa_4.html#T20" title="SCMFSA_4:th.20">SCMFSA_4:20</a></i>;<br/><b>thus </b><a NAME="E5:31_3_13"/>
<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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c3">n</font> <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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:31"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E1:31_3_13"><i><font color="Green" title="E22">A92</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span></span><br/><div><i><font color="Green" title="E25">A95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c9">c</font>
<b>by </b><i><a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="txt" href="#E4:31_3_13"><i><font color="Green" title="E24">A94</font></i></a>, <a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</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="hs2(this)" href="javascript:()" title="31_3_13_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">g</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_13_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3_13_2_1"/>
( <font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> or <font color="Maroon" title="c9">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_13_2_1_1"><b>suppose </b></a><a NAME="E1:31_3_13_2_1_1"/><i><font color="Green" title="E26">A96</font></i>: 
<font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c10">m1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:31_3_13_2_1_1"/><i><font color="Green" title="E27">A97</font></i>: 
<font color="Maroon" title="c10">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></span>)</span>
 <b>and </b><br/><a NAME="E4:31_3_13_2_1_1"/><i><font color="Green" title="E28">A98</font></i>: 
<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"><font color="Maroon" title="c8">f</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c7">da</font></span>)</span>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">m1</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">m2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:31_3_13_2_1_1"/><i><font color="Green" title="E29">A99</font></i>: 
<font color="Maroon" title="c11">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">da</font></span>)</span>
 <b>and </b><br/><a NAME="E7:31_3_13_2_1_1"/><i><font color="Green" title="E30">A100</font></i>: 
<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"><font color="Maroon" title="c8">f</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c7">da</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m2</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</a></i>;<br/><b>thus </b><a NAME="E8:31_3_13_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font>
 <b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="txt" href="#E4:31_3_13"><i><font color="Green" title="E24">A94</font></i></a>, <a class="txt" href="#E1:31_3_13_2_1_1"><i><font color="Green" title="E26">A96</font></i></a>, <a class="txt" href="#E3:31_3_13_2_1_1"><i><font color="Green" title="E27">A97</font></i></a>, <a class="txt" href="#E4:31_3_13_2_1_1"><i><font color="Green" title="E28">A98</font></i></a>, <a class="txt" href="#E6:31_3_13_2_1_1"><i><font color="Green" title="E29">A99</font></i></a>, <a class="txt" href="#E7:31_3_13_2_1_1"><i><font color="Green" title="E30">A100</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="31_3_13_2_1_2"><b>suppose </b></a><a NAME="E1:31_3_13_2_1_2"/><i><font color="Green" title="E26">A101</font></i>: 
<font color="Maroon" title="c9">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">f</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</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> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font> = 
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font>
<b>by </b><i><a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font>
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c9">g</font>
<b>by </b><i><a class="txt" href="#E3:31_3_13"><i><font color="Green" title="E23">A93</font></i></a>, <a class="txt" href="#E4:31_3_13"><i><font color="Green" title="E24">A94</font></i></a>, <a class="txt" href="#E1:31_3_13_2_1_2"><i><font color="Green" title="E26">A101</font></i></a>, <a class="ref" href="scmfsa_2.html#T101" title="SCMFSA_2:th.101">SCMFSA_2:101</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="E8:31_3_13"/>
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</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="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:31_3_13"><i><font color="Green" title="E25">A95</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" target="_self" title="SCMFSA6A:th.38">Th38</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>

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