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

<b>let </b><font color="Maroon" title="c39">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/>

<b>set </b><font color="Maroon" title="c40">p</font> = <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c41">q</font> =  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> ;<br/>
<a NAME="E1:69"/><i><font color="Green" title="E67">A1</font></i>: 
for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/> for <font color="Olive" title="b3">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s2</font> &amp; <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b1">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b1">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b1">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c42">s1</font>, <font color="Maroon" title="c43">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:69_1"/><i><font color="Green" title="E68">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c42">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c43">s2</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 )
 ;<br/>

<b>set </b><font color="Maroon" title="c45">Cs1</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font>;<br/>
<b>set </b><font color="Maroon" title="c46">Cs2</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font>;<br/>
<a NAME="E2:69_1"/><i><font color="Green" title="E69">A3</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c42">s1</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c43">s2</font> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/>
<a NAME="E3:69_1"/><i><font color="Green" title="E70">A4</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="ref" href="scmbsort.html#T47" target="_self" title="SCMBSORT:th.47">Th47</a></i>;<br/>
<a NAME="E4:69_1"/><b>then </b><i><font color="Green" title="E71">A5</font></i>: 
<font color="Maroon" title="c42">s1</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E5:69_1"/><i><font color="Green" title="E72">A6</font></i>: 
<font color="Maroon" title="c43">s2</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="scmbsort.html#E3:69_1"><i><font color="Green" title="E70">A4</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E6:69_1"/><i><font color="Green" title="E73">A7</font></i>: 
(  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c42">s1</font> &amp;  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c43">s2</font> )
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="scmbsort.html#T53" target="_self" title="SCMBSORT:th.53">Th53</a></i>;<br/>
<i><font color="Green" title="E74">A8</font></i>: <font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
1
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
<br/>.= 
<font color="Maroon" title="c43">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
;<br/>
<i><font color="Green" title="E75">A9</font></i>: <font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c39">w</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
<br/>.= 
<font color="Maroon" title="c43">s2</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
;<br/>
<i><font color="Green" title="E76">A10</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c42">s1</font> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="ref" href="ami_1.html#D41" title="AMI_1:def.41">AMI_1:def 41</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c43">s2</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="ref" href="ami_1.html#D41" title="AMI_1:def.41">AMI_1:def 41</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_1_4"/>
( <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 </span><b>by </b><i><a class="txt" href="scmbsort.html#E1:69_1"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="nat_1.html#T35" title="NAT_1:th.35">NAT_1:35</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_1"><b>suppose </b></a><a NAME="E1:69_1_4_1"/><i><font color="Green" title="E77">A11</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_1_4_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:69_1"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a></i>;<br/><b>thus </b><a NAME="E3:69_1_4_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:69_1"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_1"><i><font color="Green" title="E76">A10</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_1"><i><font color="Green" title="E77">A11</font></i></a></i>;<br/><b>thus </b><a NAME="E4:69_1_4_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:69_1"><i><font color="Green" title="E69">A3</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_1"><i><font color="Green" title="E77">A11</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_2"><b>suppose </b></a><a NAME="E1:69_1_4_2"/><i><font color="Green" title="E77">A12</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_2"><i><font color="Green" title="E77">A12</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 1
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_2"><i><font color="Green" title="E77">A12</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_2"><i><font color="Green" title="E77">A12</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_2"><i><font color="Green" title="E77">A12</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_2"><i><font color="Green" title="E77">A12</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_3"><b>suppose </b></a><a NAME="E1:69_1_4_3"/><i><font color="Green" title="E77">A13</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_3"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 2
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_3"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_3"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_3"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_3"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_4"><b>suppose </b></a><a NAME="E1:69_1_4_4"/><i><font color="Green" title="E77">A14</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_4"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 3
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_4"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_4"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_4"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_4"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_5"><b>suppose </b></a><a NAME="E1:69_1_4_5"/><i><font color="Green" title="E77">A15</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_5"><i><font color="Green" title="E77">A15</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 4
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_5"><i><font color="Green" title="E77">A15</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_5"><i><font color="Green" title="E77">A15</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_5"><i><font color="Green" title="E77">A15</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_5"><i><font color="Green" title="E77">A15</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_6"><b>suppose </b></a><a NAME="E1:69_1_4_6"/><i><font color="Green" title="E77">A16</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_6"><i><font color="Green" title="E77">A16</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 5
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_6"><i><font color="Green" title="E77">A16</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_6"><i><font color="Green" title="E77">A16</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_6"><i><font color="Green" title="E77">A16</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_6"><i><font color="Green" title="E77">A16</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_7"><b>suppose </b></a><a NAME="E1:69_1_4_7"/><i><font color="Green" title="E77">A17</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_7"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 6
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_7"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_7"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_7"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_7"><i><font color="Green" title="E77">A17</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_8"><b>suppose </b></a><a NAME="E1:69_1_4_8"/><i><font color="Green" title="E77">A18</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_8"><i><font color="Green" title="E77">A18</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 7
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_8"><i><font color="Green" title="E77">A18</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_8"><i><font color="Green" title="E77">A18</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_8"><i><font color="Green" title="E77">A18</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_8"><i><font color="Green" title="E77">A18</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_9"><b>suppose </b></a><a NAME="E1:69_1_4_9"/><i><font color="Green" title="E77">A19</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_9"><i><font color="Green" title="E77">A19</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 8
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_9"><i><font color="Green" title="E77">A19</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_9"><i><font color="Green" title="E77">A19</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_9"><i><font color="Green" title="E77">A19</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_9"><i><font color="Green" title="E77">A19</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_10"><b>suppose </b></a><a NAME="E1:69_1_4_10"/><i><font color="Green" title="E77">A20</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_10"><i><font color="Green" title="E77">A20</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 9
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_10"><i><font color="Green" title="E77">A20</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_10"><i><font color="Green" title="E77">A20</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_10"><i><font color="Green" title="E77">A20</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_10"><i><font color="Green" title="E77">A20</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_4_11"><b>suppose </b></a><a NAME="E1:69_1_4_11"/><i><font color="Green" title="E77">A21</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_11"><i><font color="Green" title="E77">A21</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 10
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_11"><i><font color="Green" title="E77">A21</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_11"><i><font color="Green" title="E77">A21</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c42">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_11"><i><font color="Green" title="E77">A21</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c43">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="txt" href="scmbsort.html#E6:69_1"><i><font color="Green" title="E73">A7</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_1_4_11"><i><font color="Green" title="E77">A21</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c42">UD</font> = <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6</span>)</span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c43">Us</font> = <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span>;<br/>
<a NAME="E2:69"/><i><font color="Green" title="E68">A22</font></i>: 
 <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T59" target="_self" title="SCMBSORT:th.59">Th59</a></i>;<br/>
<a NAME="E3:69"/><i><font color="Green" title="E69">A23</font></i>: 
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K5" title="ENUMSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6</span>)</span></span><a href="enumset1.html#K5" title="ENUMSET1:func.5">}</a></span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T58" target="_self" title="SCMBSORT:th.58">Th58</a></i>;<br/>
<a NAME="E4:69"/><b>then </b><i><font color="Green" title="E70">A24</font></i>: 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6</span>)</span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69"><i><font color="Green" title="E68">A22</font></i></a>, <a class="ref" href="enumset1.html#T62" title="ENUMSET1:th.62">ENUMSET1:62</a></i>;<br/>
<a NAME="E5:69"/><i><font color="Green" title="E71">A25</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">s1</font>, <font color="Olive" title="b3">s2</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st 11 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s2</font> holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b3">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b3">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c45">s1</font>, <font color="Maroon" title="c46">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:69_2"/><i><font color="Green" title="E72">A26</font></i>: 
11 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font>
 <b>and </b><br/><a NAME="E2:69_2"/><i><font color="Green" title="E73">A27</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c45">s1</font>
 <b>and </b><br/><a NAME="E3:69_2"/><i><font color="Green" title="E74">A28</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c46">s2</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c47">Cs11</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11;<br/>
<b>set </b><font color="Maroon" title="c48">Cs21</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11;<br/>
<a NAME="E4:69_2"/><i><font color="Green" title="E75">A29</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="ref" href="scmbsort.html#T47" target="_self" title="SCMBSORT:th.47">Th47</a></i>;<br/>
<a NAME="E5:69_2"/><b>then </b><i><font color="Green" title="E76">A30</font></i>: 
<font color="Maroon" title="c45">s1</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2"><i><font color="Green" title="E73">A27</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E6:69_2"/><i><font color="Green" title="E77">A31</font></i>: 
<font color="Maroon" title="c46">s2</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 0
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:69_2"><i><font color="Green" title="E74">A28</font></i></a>, <a class="txt" href="scmbsort.html#E4:69_2"><i><font color="Green" title="E75">A29</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E7:69_2"/><i><font color="Green" title="E78">A32</font></i>: 
 <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c45">s1</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2"><i><font color="Green" title="E73">A27</font></i></a>, <a class="ref" href="scmbsort.html#T53" target="_self" title="SCMBSORT:th.53">Th53</a></i>;<br/>
<a NAME="E8:69_2"/><i><font color="Green" title="E79">A33</font></i>: 
 <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c46">s2</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:69_2"><i><font color="Green" title="E74">A28</font></i></a>, <a class="ref" href="scmbsort.html#T53" target="_self" title="SCMBSORT:th.53">Th53</a></i>;<br/>
<i><font color="Green" title="E80">A34</font></i>: <font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
1
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2"><i><font color="Green" title="E73">A27</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
<br/>.= 
<font color="Maroon" title="c46">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E3:69_2"><i><font color="Green" title="E74">A28</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
;<br/>
<i><font color="Green" title="E81">A35</font></i>: <font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> = 
<font color="Maroon" title="c39">w</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2"><i><font color="Green" title="E73">A27</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
<br/>.= 
<font color="Maroon" title="c46">s2</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E3:69_2"><i><font color="Green" title="E74">A28</font></i></a>, <a class="ref" href="scmbsort.html#T54" target="_self" title="SCMBSORT:th.54">Th54</a></i>
;<br/>
<a NAME="E11:69_2"/><i><font color="Green" title="E82">A36</font></i>: 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T56" target="_self" title="SCMBSORT:th.56">Th56</a></i>;<br/>
<a NAME="E12:69_2"/><i><font color="Green" title="E83">A37</font></i>: 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T56" target="_self" title="SCMBSORT:th.56">Th56</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_2_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c49">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:69_2_3"/>
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span>
 ;<br/><a NAME="E2:69_2_3"/><b>then </b><i><font color="Green" title="E84">A38</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6</span>)</span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:69"><i><font color="Green" title="E68">A22</font></i></a>, <a class="txt" href="scmbsort.html#E3:69"><i><font color="Green" title="E69">A23</font></i></a>, <a class="ref" href="enumset1.html#T62" title="ENUMSET1:th.62">ENUMSET1:62</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_2_3_1"/>
( <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5 or <font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6 )
 </span><b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2_3"><i><font color="Green" title="E84">A38</font></i></a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_1"><b>suppose </b></a><a NAME="E1:69_2_3_1_1"/><i><font color="Green" title="E85">A39</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E10:69_2"><i><font color="Green" title="E81">A35</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_1"><i><font color="Green" title="E85">A39</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_2"><b>suppose </b></a><a NAME="E1:69_2_3_1_2"/><i><font color="Green" title="E85">A40</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_2"><i><font color="Green" title="E85">A40</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_3"><b>suppose </b></a><a NAME="E1:69_2_3_1_3"/><i><font color="Green" title="E85">A41</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E10:69_2"><i><font color="Green" title="E81">A35</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_3"><i><font color="Green" title="E85">A41</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_4"><b>suppose </b></a><a NAME="E1:69_2_3_1_4"/><i><font color="Green" title="E85">A42</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_4"><i><font color="Green" title="E85">A42</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_5"><b>suppose </b></a><a NAME="E1:69_2_3_1_5"/><i><font color="Green" title="E85">A43</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 3
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_5"><i><font color="Green" title="E85">A43</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_6"><b>suppose </b></a><a NAME="E1:69_2_3_1_6"/><i><font color="Green" title="E85">A44</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 4
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_6"><i><font color="Green" title="E85">A44</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_7"><b>suppose </b></a><a NAME="E1:69_2_3_1_7"/><i><font color="Green" title="E85">A45</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 5
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_7"><i><font color="Green" title="E85">A45</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_2_3_1_8"><b>suppose </b></a><a NAME="E1:69_2_3_1_8"/><i><font color="Green" title="E85">A46</font></i>: 
<font color="Maroon" title="c49">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 6
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font> = 
<font color="Maroon" title="c45">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c49">x</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E9:69_2"><i><font color="Green" title="E80">A34</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_2_3_1_8"><i><font color="Green" title="E85">A46</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E14:69_2"/><b>then </b><i><font color="Green" title="E84">A47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E11:69_2"><i><font color="Green" title="E82">A36</font></i></a>, <a class="txt" href="scmbsort.html#E12:69_2"><i><font color="Green" title="E83">A37</font></i></a>, <a class="ref" href="funct_1.html#T165" title="FUNCT_1:th.165">FUNCT_1:165</a></i>;<br/>
<i><font color="Green" title="E85">A48</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> 11
<b>by </b><i><a class="txt" href="scmbsort.html#E5:69_2"><i><font color="Green" title="E76">A30</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 11</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:69_2"><i><font color="Green" title="E77">A31</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E69"><i><font color="Green" title="E48">Lm2</font></i></a></i>
;<br/>
<a NAME="E16:69_2"/><i><font color="Green" title="E86">A49</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> 
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:69_2"><i><font color="Green" title="E73">A27</font></i></a>, <a class="ref" href="scmbsort.html#T66" target="_self" title="SCMBSORT:th.66">Th66</a></i>;<br/>
<a NAME="E17:69_2"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> 
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:69_2"><i><font color="Green" title="E74">A28</font></i></a>, <a class="ref" href="scmbsort.html#T66" target="_self" title="SCMBSORT:th.66">Th66</a></i>;<br/>
<b>hence </b><a NAME="E18:69_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c44">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69_2"><i><font color="Green" title="E72">A26</font></i></a>, <a class="txt" href="scmbsort.html#E7:69_2"><i><font color="Green" title="E78">A32</font></i></a>, <a class="txt" href="scmbsort.html#E8:69_2"><i><font color="Green" title="E79">A33</font></i></a>, <a class="txt" href="scmbsort.html#E14:69_2"><i><font color="Green" title="E84">A47</font></i></a>, <a class="txt" href="scmbsort.html#E15:69_2"><i><font color="Green" title="E85">A48</font></i></a>, <a class="txt" href="scmbsort.html#E16:69_2"><i><font color="Green" title="E86">A49</font></i></a>, <a class="ref" href="scmbsort.html#T26" target="_self" title="SCMBSORT:th.26">Th26</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c44">DD</font> = <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>;<br/>
<a NAME="E6:69"/><i><font color="Green" title="E72">A50</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T42" target="_self" title="SCMBSORT:th.42">Th42</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c45">s1</font>, <font color="Maroon" title="c46">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c47">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:69_3"/><i><font color="Green" title="E73">A51</font></i>: 
( <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c45">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c46">s2</font> )
 ;<br/><b>set </b><font color="Maroon" title="c48">Cs1i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font>;<br/><b>set </b><font color="Maroon" title="c49">Cs2i</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font>;<br/><a NAME="E2:69_3"/>
(  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c45">s1</font> &amp;  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c46">s2</font> )
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a>, <a class="ref" href="scmbsort.html#T53" target="_self" title="SCMBSORT:th.53">Th53</a></i>;<br/><a NAME="E3:69_3"/><b>then </b><i><font color="Green" title="E74">A52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#T124" title="AMI_1:th.124">AMI_1:124</a></i>;<br/><a NAME="E4:69_3"/><i><font color="Green" title="E75">A53</font></i>: 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmbsort.html#T55" target="_self" title="SCMBSORT:th.55">Th55</a></i>;<br/><a NAME="E5:69_3"/><i><font color="Green" title="E76">A54</font></i>: 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmbsort.html#T55" target="_self" title="SCMBSORT:th.55">Th55</a></i>;<br/><a NAME="E6:69_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:69_3_1"/><i><font color="Green" title="E77">A55</font></i>: 
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69"><i><font color="Green" title="E70">A24</font></i></a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></i>;<br/>
<a NAME="E2:69_3_1"/><i><font color="Green" title="E78">A56</font></i>: 
 <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E4:69"><i><font color="Green" title="E70">A24</font></i></a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></i>;<br/>
<a NAME="E3:69_3_1"/><i><font color="Green" title="E79">A57</font></i>: 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T56" target="_self" title="SCMBSORT:th.56">Th56</a></i>;<br/>
<a NAME="E4:69_3_1"/><i><font color="Green" title="E80">A58</font></i>: 
<span class="p1">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T56" target="_self" title="SCMBSORT:th.56">Th56</a></i>;<br/>
<a NAME="E5:69_3_1"/><i><font color="Green" title="E81">A59</font></i>: 
( <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10 implies 10 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c47">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c50">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:69_3_1_1"/><i><font color="Green" title="E82">A60</font></i>: 
<font color="Maroon" title="c50">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_1_1"/>
( <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 or <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  or <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0 )
 </span><b>by </b><i><a class="txt" href="scmbsort.html#E1:69_3_1_1"><i><font color="Green" title="E82">A60</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="69_3_1_1_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_1"/><i><font color="Green" title="E83">A61</font></i>: 
<font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_1_1_1_1_1"/>
( <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 or <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_3_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_1"><i><font color="Green" title="E83">A61</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10
 ;<br/><div class="add"><a NAME="E2:69_3_1_1_1_1_1_1_2"/><b>then </b>
11 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c47">i</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69_3_1"><i><font color="Green" title="E81">A59</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:69_3_1_1_1_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69"><i><font color="Green" title="E71">A25</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a></i>;<br/><b>hence </b><a NAME="E4:69_3_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69_3_1"><i><font color="Green" title="E77">A55</font></i></a>, <a class="txt" href="scmbsort.html#E3:69_3_1"><i><font color="Green" title="E79">A57</font></i></a>, <a class="txt" href="scmbsort.html#E4:69_3_1"><i><font color="Green" title="E80">A58</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_1"><i><font color="Green" title="E83">A61</font></i></a>, <a class="ref" href="funct_1.html#T165" title="FUNCT_1:th.165">FUNCT_1:165</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:69_3_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_2"/><i><font color="Green" title="E83">A62</font></i>: 
<font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_1_1_2_1_1"/>
( <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 or <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_3_1_1_1_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_2"><i><font color="Green" title="E83">A62</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10
 ;<br/><div class="add"><a NAME="E2:69_3_1_1_1_2_1_1_2"/><b>then </b>
11 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c47">i</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69_3_1"><i><font color="Green" title="E81">A59</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E3:69_3_1_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69"><i><font color="Green" title="E71">A25</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_2"><i><font color="Green" title="E83">A62</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:69_3_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_3"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_3"/><i><font color="Green" title="E83">A63</font></i>: 
<font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3_1_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_3_1_1_1_3_1_1"/>
( <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10 or <font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_3_1_1_1"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 10
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_3_1_1_1_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:69"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_3"><i><font color="Green" title="E83">A63</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_3_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:69_3_1_1_1_3_1_1_2"/>
<font color="Maroon" title="c47">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 10
 ;<br/><div class="add"><a NAME="E2:69_3_1_1_1_3_1_1_2"/><b>then </b>
11 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c47">i</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69_3_1"><i><font color="Green" title="E81">A59</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:69_3_1_1_1_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E5:69"><i><font color="Green" title="E71">A25</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3"><i><font color="Green" title="E73">A51</font></i></a></i>;<br/><b>hence </b><a NAME="E4:69_3_1_1_1_3_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:69_3_1"><i><font color="Green" title="E78">A56</font></i></a>, <a class="txt" href="scmbsort.html#E3:69_3_1"><i><font color="Green" title="E79">A57</font></i></a>, <a class="txt" href="scmbsort.html#E4:69_3_1"><i><font color="Green" title="E80">A58</font></i></a>, <a class="txt" href="scmbsort.html#E1:69_3_1_1_1_3"><i><font color="Green" title="E83">A63</font></i></a>, <a class="ref" href="funct_1.html#T165" title="FUNCT_1:th.165">FUNCT_1:165</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:69_3_1_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:69_3_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E4:69_3"><i><font color="Green" title="E75">A53</font></i></a>, <a class="txt" href="scmbsort.html#E5:69_3"><i><font color="Green" title="E76">A54</font></i></a>, <a class="ref" href="funct_1.html#T165" title="FUNCT_1:th.165">FUNCT_1:165</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E7:69_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c45">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c46">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c47">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E6:69"><i><font color="Green" title="E72">A50</font></i></a>, <a class="txt" href="scmbsort.html#E3:69_3"><i><font color="Green" title="E74">A52</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:69"/><b>then </b>
for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s1</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s2</font> holds <br/>for <font color="Olive" title="b3">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b1">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Olive" title="b2">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E9:69"/>
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">w</font></span>)</span> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a></i>;<br/>


</div>
