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

<b>set </b><font color="Maroon">D</font> = <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> ;<br/>
<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="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c</font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>



<b>assume </b><a NAME="E1:123"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 ;<br/>

<b>assume </b><a NAME="E2:123"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>

<b>set </b><font color="Maroon">P</font> =  <a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span>;<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>for <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>   st <font color="Olive">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>,<font color="Olive">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>;<br/>
<a NAME="E3:123"/>
 <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="scmfsa7b.html#R3">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T13">SCMFSA7B:13</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">I</font> =  <a href="scmfsa6a.html#K2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> as  <a href="scmfsa6b.html#V2">parahalting</a> <a href="scmfsa7b.html#V1">good</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a> <b>by </b><i><a class="ref" href="scmfsa8c.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E5:123"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1"><b>proof </b></a><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>set </b><font color="Maroon">s0</font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</font>;<br/>
<b>assume </b><a NAME="E1:123_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:123_1"/><b>then </b>
( <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> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <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> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>;<br/>
<a NAME="E3:123_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<font color="Maroon">I</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="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="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">s</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="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T42" target="_self">Th42</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></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> <font color="Maroon">b</font>
<b>by </b><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">b</font>
<b>by </b><i>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E6:123"/><i><font color="Green">E45</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="123_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><a NAME="E1:123_2"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/>

<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>assume </b><a NAME="E2:123_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<i><font color="Green">E49</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> = 
<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> <font color="Maroon">a</font>,<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">I</font>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T7">SCMFSA6C:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</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#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</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> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T6">SCMFSA6C:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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">c</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>
<i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<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> <font color="Maroon">a</font>,<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">I</font>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T7">SCMFSA6C:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">I</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</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#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</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> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T6">SCMFSA6C:6</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">c</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>
<a NAME="E5:123_2"/>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E6:123_2"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E7:123_2"/>
 <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="scmfsa7b.html#T13">SCMFSA7B:13</a></i>;<br/>
<a NAME="E8:123_2"/><b>then </b>
<font color="Maroon">I</font> <a href="scmfsa7b.html#R4">does_not_destroy</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E9:123_2"/><b>then </b><i><font color="Green">E52</font></i>: 
( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</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"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span>,<font color="Maroon">s</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="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"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</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>, </i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<font color="Maroon">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<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#K6">-</a> 1</span>)</span></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E11:123_2"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:123"/><i><font color="Green">E53</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  <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>(, );<br/></i>
<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="E9:123"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">sa</font>]
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:123"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K2" target="_self">Times</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
 ;<br/>


</div>
