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

<b>let </b><font color="Maroon">s1</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">s2</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="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">Ig</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">Ig</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">s1</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
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:55"/><i><font color="Green">E36</font></i>: 
 <a href="scmfsa9a.html#R3" target="_self">ProperBodyWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font>
 <b>and </b><br/><a NAME="E4:55"/><i><font color="Green">E40</font></i>: 
 <a href="scmfsa9a.html#R4" target="_self">WithVariantWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font>
 ;<br/>

<b>set </b><font color="Maroon">SW1</font> =  <a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font>;<br/>
<b>set </b><font color="Maroon">SW2</font> =  <a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:55"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">f</font> is <a href="scmfsa9a.html#V1" target="_self">on_data_only</a>
 <b>and </b><br/><a NAME="E7:55"/><i><font color="Green">E42</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>   holds <br/>( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">k</font></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 <b>by </b><i>, <a class="ref" href="scmfsa9a.html#T7" target="_self">Th7</a>, , </i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="scmfsa9a.html#D5" target="_self">SCMFSA9A:def 5</a><br/>

<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/>

<a NAME="E8:55"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></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="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></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="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa9a.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E9:55"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>
<a NAME="E10:55"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</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="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</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="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa9a.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E11:55"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s1</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="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</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> )
 
<b>by </b><i>, <a class="ref" href="scmfsa9a.html#T9" target="_self">Th9</a>, </i>;<br/>
<b>hence </b><a NAME="E12:55"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</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="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K5">StepWhile&gt;0</a> <font color="Maroon">a</font>,<font color="Maroon">Ig</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 <b>by </b><i><a class="ref" href="scmfsa9a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa9a.html#T10" target="_self">Th10</a></i>;<br/>


</div>
