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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">J</font> be  <a href="scmfsa7b.html#V1">good</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>





<b>set </b><font color="Maroon">I</font> = <font color="Maroon">J</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 or  not <font color="Maroon">a</font> is <a href="sf_mastr.html#V1">read-only</a> )
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E36</font></i>: 
 <a href="sfmastr2.html#R1" target="_self">ProperTimesBody</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font>
 ;<br/>

<b>set </b><font color="Maroon">ST</font> =  <a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">au</font> = 1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">Is</font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">SW</font> =  <a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<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">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span>;<br/>
<a NAME="E3:22"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0 or  not <font color="Maroon">a</font> is <a href="sf_mastr.html#V1">read-only</a> )
 
<b>by </b><i><a class="ref" href="sf_mastr.html#D5">SF_MASTR:def 5</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</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> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> );<br/>
<a NAME="E4:22"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 = 
<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">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_9.html#D5">SCMFSA_9:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E5:22"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> )
 <b>and </b><br/><a NAME="E2:22_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">sa</font> = <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E4:22_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">sa</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E5:22_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:22_2"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa7b.html#R5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E7:22_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa7b.html#R6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E8:22_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E9:22_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E10:22_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#D6">SCMFSA6A:def 6</a></i>;<br/>
<a NAME="E11:22_2"/><i><font color="Green">E77</font></i>: 
 <a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a></i>;<br/>
<a NAME="E12:22_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="sfmastr1.html#T3">SFMASTR1:3</a></i>;<br/>
<a NAME="E13:22_2"/>
 <a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/>
<a NAME="E14:22_2"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span>
 
<b>by </b><i>, , , , <a class="ref" href="sfmastr1.html#T4">SFMASTR1:4</a></i>;<br/>
<a NAME="E15:22_2"/>
not 1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="sfmastr1.html#T21">SFMASTR1:21</a></i>;<br/>
<a NAME="E16:22_2"/><b>then </b><i><font color="Green">E80</font></i>: 
not 1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p0">(<span class="default"><span class="p1"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p0">(<span class="default"><span class="p1"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">a</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><a NAME="E2:22_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p0">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">a</font></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E3:22_2_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E18:22_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p0">(<span class="default"><span class="p1"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p0">(<span class="default"><span class="p1"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">a</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="scmfsa9a.html#T38">SCMFSA9A:38</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="sfmastr1.html#T12">SFMASTR1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">J</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i>, , <a class="ref" href="scmfsa8c.html#T96">SCMFSA8C:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>
<b>hence </b><a NAME="E20:22_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">a</font>,<font color="Maroon">J</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E6:22"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );</i><br/>


</div>
