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

<span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">b</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font> &amp; <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c5">i0</font> = <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">i1</font> = <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">i2</font> = <font color="Maroon" title="c4">b</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">i01</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span>;<br/>
<a NAME="E1:35"/>
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K1" title="SF_MASTR:func.1">UsedIntLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T32" title="SF_MASTR:th.32">SF_MASTR:32</a></span>;<br/>
<a NAME="E2:35"/><span class="kw">then </span>
 <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T18" title="SF_MASTR:th.18">SF_MASTR:18</a></span>;<br/>
<a NAME="E3:35"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A1</font></span>: 
not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T54" title="SF_MASTR:th.54">SF_MASTR:54</a></span>;<br/>
<a NAME="E4:35"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E5:35"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font></span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_1_1_1"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font></span><br/><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T7" target="_self" title="SCMFSA6C:th.7">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T9" target="_self" title="SCMFSA6C:th.9">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" target="_self" title="SCMFSA6C:th.3">Th3</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_1_1_2"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font></span><br/><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T7" target="_self" title="SCMFSA6C:th.7">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T9" target="_self" title="SCMFSA6C:th.9">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1_2"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="scmfsa6c.html#T3" target="_self" title="SCMFSA6C:th.3">Th3</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmfsa6c.html#K2" title="SCMFSA6C:func.2">swap</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T7" target="_self" title="SCMFSA6C:th.7">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T9" target="_self" title="SCMFSA6C:th.9">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Macro</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T89" title="SCMFSA_2:th.89">SCMFSA_2:89</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" target="_self" title="SCMFSA6C:th.3">Th3</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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