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

<span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b2">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b2">I</font></span>)</span>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b1">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b1">I</font></span>)</span>)</span>)</span>)</span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c5">D</font> =  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</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="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> implies  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)</span>)</span>)</span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">I0</font> =  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">I1</font> = <font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">s2</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">P2</font> = <font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s10</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">P10</font> = <font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">k</font> =  <a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>);<br/>
<span class="kw">assume </span><a NAME="E1:29"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)</span>)</span>)</span>)</span></span><br/>

<a NAME="E2:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A3</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8c.html#T29" target="_self" title="SCMFSA8C:th.29">Th58</a></span>;<br/>
<a NAME="E3:29"/>
<font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="scmfsa8c.html#T29" target="_self" title="SCMFSA8C:th.29">Th58</a></span>;<br/>
<a NAME="E4:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#D7" title="SCMFSA7B:def.7">SCMFSA7B:def 7</a></span>;<br/>
<a NAME="E5:29"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="scmfsa8c.html#T29" target="_self" title="SCMFSA8C:th.29">Th58</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:29"/>
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K2" title="SCMFSA8A:func.2">pseudo-LifeSpan</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">I</font></span>)</span>)</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
