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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:90"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E2:90"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E3:90"/><i><font color="Green">E63</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> implies (  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) ) );<br/>
<a NAME="E4:90"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:90_1"/><i><font color="Green">E65</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<i><font color="Green">E66</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="sf_mastr.html#T67" target="_self">Th67</a></i>
;<br/>
<i><font color="Green">E67</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="sf_mastr.html#T67" target="_self">Th67</a></i>
;<br/>
<b>hence </b><a NAME="E4:90_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:90"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="sf_mastr.html#E2:90_1"><i><font color="Green">E66</font></i></a></i>;<br/>

<b>thus </b><a NAME="E5:90_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:90_1"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_1"><i><font color="Green">E67</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:90_1_3"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_1_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:90"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_1_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/>

<b>assume </b><a NAME="E7:90_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E7:90_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:90"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sf_mastr.html#E7:90_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<div><i><font color="Green">E65</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="90_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:90_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font>]
 ;<br/><b>thus </b><a NAME="E2:90_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_2_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1;<br/>
<b>assume </b><a NAME="E1:90_2_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:90_2_1"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<i><font color="Green">E69</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/>
<i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/>
<a NAME="E5:90_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T64" target="_self">Th64</a></i>;<br/>
<a NAME="E6:90_2_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/>
<a NAME="E7:90_2_1"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:90_2_1"/><b>then </b><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E9:90_2_1"/><b>then </b><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E10:90_2_1"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E8:90_2_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E11:90_2_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sf_mastr.html#E2:90_2_1"><i><font color="Green">E68</font></i></a></i>;<br/>
<a NAME="E12:90_2_1"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E9:90_2_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E13:90_2_1"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T23" target="_self">Th23</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_2_1_3"><b>now </b></a><div class="add"><b>thus </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:90_2_1_3"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E3:90_2_1_3"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1_3"><i><font color="Green">E76</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_2_1_3"><i><font color="Green">E76</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E15:90_2_1"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<i><font color="Green">E77</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E13:90_2_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E13:90_2_1"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E15:90_2_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
;<br/>
<a NAME="E17:90_2_1"/><i><font color="Green">E78</font></i>: 
 <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E12:90_2_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="sf_mastr.html#T39" target="_self">Th39</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_2_1_5"><b>now </b></a><div class="add"><b>thus </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:90_2_1_5"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E3:90_2_1_5"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_2_1_5"><i><font color="Green">E79</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E19:90_2_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E17:90_2_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E17:90_2_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="sf_mastr.html#E19:90_2_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
;<br/>
<a NAME="E21:90_2_1"/><b>then </b><i><font color="Green">E80</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E16:90_2_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="sf_mastr.html#T72" target="_self">Th72</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E22:90_2_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:90"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E10:90_2_1"><i><font color="Green">E73</font></i></a></i>;<br/>

<b>thus </b><a NAME="E23:90_2_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E8:90_2_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E9:90_2_1"><i><font color="Green">E72</font></i></a>, <a class="txt" href="sf_mastr.html#E21:90_2_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:90_2_1_7"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_2_1_7_1"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> or  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_7_1_1"><b>suppose </b></a><a NAME="E1:90_2_1_7_1_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E10:90_2_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sf_mastr.html#E21:90_2_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1_7_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_7_1_2"><b>suppose </b></a><a NAME="E1:90_2_1_7_1_2"/><i><font color="Green">E82</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sf_mastr.html#T68" target="_self">Th68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1_7"><i><font color="Green">E81</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E10:90_2_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1_7_1_2"><i><font color="Green">E82</font></i></a>, <a class="ref" href="sf_mastr.html#T68" target="_self">Th68</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/>

<b>assume </b><a NAME="E25:90_2_1"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_8"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_2_1_8"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> or  not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_8_1"><b>suppose </b></a><a NAME="E1:90_2_1_8_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E10:90_2_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sf_mastr.html#E21:90_2_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1_8_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_8_2"><b>suppose </b></a><a NAME="E1:90_2_1_8_2"/><i><font color="Green">E82</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_2_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sf_mastr.html#T70" target="_self">Th70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E25:90_2_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E4:90_2_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E10:90_2_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_2_1_8_2"><i><font color="Green">E82</font></i></a>, <a class="ref" href="sf_mastr.html#T70" target="_self">Th70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:90"/><i><font color="Green">E66</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="sf_mastr.html#E4:90"><i><font color="Green">E64</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90"><i><font color="Green">E65</font></i></a>);<br/></i>
<b>hence </b><a NAME="E7:90"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E8:90"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_3"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_1"><b>suppose </b></a><a NAME="E1:90_3_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><i><font color="Green">E69</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="sf_mastr.html#T67" target="_self">Th67</a></i>
;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="sf_mastr.html#T67" target="_self">Th67</a></i>
;<br/><b>hence </b><a NAME="E4:90_3_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E2:90_3_1"><i><font color="Green">E69</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:90_3_1_3"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1_3"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:90"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_1_3"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>assume </b><a NAME="E6:90_3_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:90_3_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:90"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E1:90_3_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2"><b>suppose </b></a><a NAME="E1:90_3_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:90_3_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1;<br/><a NAME="E4:90_3_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E8:90"><i><font color="Green">E67</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/><i><font color="Green">E71</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
;<br/><a NAME="E7:90_3_2"/><i><font color="Green">E72</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:90"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a></i>;<br/><a NAME="E8:90_3_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T64" target="_self">Th64</a></i>;<br/><a NAME="E9:90_3_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/><a NAME="E10:90_3_2"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E1:90"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E11:90_3_2"/><b>then </b><i><font color="Green">E73</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/><a NAME="E12:90_3_2"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E7:90_3_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><a NAME="E13:90_3_2"/><b>then </b><i><font color="Green">E75</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E7:90_3_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="sf_mastr.html#E11:90_3_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>;<br/><a NAME="E14:90_3_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:90"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a></i>;<br/><a NAME="E15:90_3_2"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E12:90_3_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E16:90_3_2"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T23" target="_self">Th23</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_3_2_3"><b>now </b></a><div class="add"><b>thus </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:90_3_2_3"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E3:90_3_2_3"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2_3"><i><font color="Green">E78</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:90"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_3_2_3"><i><font color="Green">E78</font></i></a></i>
;<br/></div><b>end;</b></div><a NAME="E18:90_3_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><i><font color="Green">E79</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E16:90_3_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E16:90_3_2"><i><font color="Green">E77</font></i></a>, <a class="txt" href="sf_mastr.html#E18:90_3_2"><i><font color="Green">E78</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
;<br/><a NAME="E20:90_3_2"/><i><font color="Green">E80</font></i>: 
 <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E15:90_3_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="sf_mastr.html#T39" target="_self">Th39</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_3_2_5"><b>now </b></a><div class="add"><b>thus </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>
;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:90_3_2_5"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E3:90_3_2_5"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2_5"><i><font color="Green">E81</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:90"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E3:90_3_2_5"><i><font color="Green">E81</font></i></a></i>
;<br/></div><b>end;</b></div><a NAME="E22:90_3_2"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><i><font color="Green">E82</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E20:90_3_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E20:90_3_2"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sf_mastr.html#E22:90_3_2"><i><font color="Green">E81</font></i></a>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
;<br/><a NAME="E24:90_3_2"/><b>then </b><i><font color="Green">E83</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E7:90_3_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="sf_mastr.html#E19:90_3_2"><i><font color="Green">E79</font></i></a>, <a class="ref" href="sf_mastr.html#T72" target="_self">Th72</a></i>;<br/><b>thus </b><a NAME="E25:90_3_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90_3_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E7:90_3_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="sf_mastr.html#E13:90_3_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E19:90_3_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="sf_mastr.html#E23:90_3_2"><i><font color="Green">E82</font></i></a>, <a class="ref" href="sf_mastr.html#T72" target="_self">Th72</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:90_3_2_7"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_3_2_7_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> or  not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_7_1_1"><b>suppose </b></a><a NAME="E1:90_3_2_7_1_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90_3_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E13:90_3_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E24:90_3_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_7_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_7_1_2"><b>suppose </b></a><a NAME="E1:90_3_2_7_1_2"/><i><font color="Green">E85</font></i>: 
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90_3_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="sf_mastr.html#T68" target="_self">Th68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:90"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_7"><i><font color="Green">E84</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E13:90_3_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_7_1_2"><i><font color="Green">E85</font></i></a>, <a class="ref" href="sf_mastr.html#T68" target="_self">Th68</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>assume </b><a NAME="E1:90_3_2_8"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_8_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_3_2_8_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> or  not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_8_1_1"><b>suppose </b></a><a NAME="E1:90_3_2_8_1_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90_3_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E13:90_3_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E24:90_3_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_8_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_3_2_8_1_2"><b>suppose </b></a><a NAME="E1:90_3_2_8_1_2"/><i><font color="Green">E85</font></i>: 
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E5:90_3_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="sf_mastr.html#T70" target="_self">Th70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:90"><i><font color="Green">E66</font></i></a>, <a class="txt" href="sf_mastr.html#E4:90_3_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_8"><i><font color="Green">E84</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E3:90_3_2"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sf_mastr.html#E6:90_3_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="sf_mastr.html#E13:90_3_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sf_mastr.html#E1:90_3_2_8_1_2"><i><font color="Green">E85</font></i></a>, <a class="ref" href="sf_mastr.html#T70" target="_self">Th70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
