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

<span class="kw">let </span><font color="Maroon" title="c1">i</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/>

<a NAME="E1:8"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T35" title="SCMFSA_2:th.35">SCMFSA_2:35</a></span>;<br/>
<a NAME="E2:8"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
(  not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">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="c1">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="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/>
<a NAME="E3:8"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
(  not  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">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="c1">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="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:8_1"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">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="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E5">A3</font></span></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></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_1"><span class="kw">suppose </span></a><a NAME="E1:8_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T122" title="SCMFSA_2:th.122">SCMFSA_2:122</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_1"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_2"><span class="kw">suppose </span></a><a NAME="E1:8_1_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T54" title="SCMFSA_2:th.54">SCMFSA_2:54</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_2"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T9" title="SCMFSA_4:th.9">SCMFSA_4:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_3"><span class="kw">suppose </span></a><a NAME="E1:8_1_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_3"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T55" title="SCMFSA_2:th.55">SCMFSA_2:55</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_3"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T10" title="SCMFSA_4:th.10">SCMFSA_4:10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_4"><span class="kw">suppose </span></a><a NAME="E1:8_1_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_4"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T56" title="SCMFSA_2:th.56">SCMFSA_2:56</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_4"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T11" title="SCMFSA_4:th.11">SCMFSA_4:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_5"><span class="kw">suppose </span></a><a NAME="E1:8_1_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_5"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T57" title="SCMFSA_2:th.57">SCMFSA_2:57</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_5"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T12" title="SCMFSA_4:th.12">SCMFSA_4:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_6"><span class="kw">suppose </span></a><a NAME="E1:8_1_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_6"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T58" title="SCMFSA_2:th.58">SCMFSA_2:58</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_6"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T13" title="SCMFSA_4:th.13">SCMFSA_4:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_7"><span class="kw">suppose </span></a><a NAME="E1:8_1_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">l</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> <span class="kw"> such that </span><br/><a NAME="E3:8_1_7"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T59" title="SCMFSA_2:th.59">SCMFSA_2:59</a></span>;<br/><span class="kw">thus </span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
 <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_7"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="scmfsa_4.html#T14" title="SCMFSA_4:th.14">SCMFSA_4:14</a></span>
<br/>.= 
<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_7"><span class="lab"><font color="Green" title="E6">A4</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_8"><span class="kw">suppose </span></a><a NAME="E1:8_1_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">l</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> , <font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:8_1_8"/><span class="lab"><font color="Green" title="E6">A5</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></span>;<br/><span class="kw">thus </span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_8"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="scmfsa_4.html#T15" title="SCMFSA_4:th.15">SCMFSA_4:15</a></span>
<br/>.= 
<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_8"><span class="lab"><font color="Green" title="E6">A5</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_9"><span class="kw">suppose </span></a><a NAME="E1:8_1_9"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">l</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> , <font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:8_1_9"/><span class="lab"><font color="Green" title="E6">A6</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></span>;<br/><span class="kw">thus </span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_9"><span class="lab"><font color="Green" title="E6">A6</font></span></a>, <a class="ref" href="scmfsa_4.html#T16" title="SCMFSA_4:th.16">SCMFSA_4:16</a></span>
<br/>.= 
<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_9"><span class="lab"><font color="Green" title="E6">A6</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_10"><span class="kw">suppose </span></a><a NAME="E1:8_1_10"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_10"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T62" title="SCMFSA_2:th.62">SCMFSA_2:62</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_10"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T17" title="SCMFSA_4:th.17">SCMFSA_4:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_11"><span class="kw">suppose </span></a><a NAME="E1:8_1_11"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_11"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T63" title="SCMFSA_2:th.63">SCMFSA_2:63</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_11"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T18" title="SCMFSA_4:th.18">SCMFSA_4:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_12"><span class="kw">suppose </span></a><a NAME="E1:8_1_12"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_12"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T64" title="SCMFSA_2:th.64">SCMFSA_2:64</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_12"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T19" title="SCMFSA_4:th.19">SCMFSA_4:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_13"><span class="kw">suppose </span></a><a NAME="E1:8_1_13"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font></span><br/><div class="add"><a NAME="E2:8_1_13"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_13"/>
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <font color="Maroon" title="c1">i</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_4.html#T20" title="SCMFSA_4:th.20">SCMFSA_4:20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
