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

<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a>   <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a>   <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a>   <a href="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_5.html#V2" title="AMISTD_5:attr.2">relocable</a>   <a href="amistd_5.html#V3" title="AMISTD_5:attr.3">IC-recognized</a>   <a href="amistd_5.html#V5" title="AMISTD_5:attr.5">relocable1</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>  st <font color="Olive" title="b1">S</font> is  <a href="amistd_5.html#V5" title="AMISTD_5:attr.5">relocable1</a>  &amp; <font color="Olive" title="b1">S</font> is  <a href="amistd_5.html#V6" title="AMISTD_5:attr.6">relocable2</a>  &amp; <font color="Olive" title="b1">S</font> is  <a href="amistd_5.html#V4" title="AMISTD_5:attr.4">CurIns-recognized</a>  &amp; <font color="Olive" title="b1">S</font> is  <a href="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>  holds <br/> for <font color="Olive" title="b2">q</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>2</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>2</sub></font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Olive" title="b1">S</font>  st  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">p</font> holds <br/> for <font color="Olive" title="b4">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b4">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">k</font>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a>   <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a>   <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a>   <a href="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="amistd_5.html#V2" title="AMISTD_5:attr.2">relocable</a>   <a href="amistd_5.html#V3" title="AMISTD_5:attr.3">IC-recognized</a>   <a href="amistd_5.html#V5" title="AMISTD_5:attr.5">relocable1</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V5" title="AMISTD_5:attr.5">relocable1</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V6" title="AMISTD_5:attr.6">relocable2</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V4" title="AMISTD_5:attr.4">CurIns-recognized</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>  implies  for <font color="Olive" title="b1">q</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">p</font> holds <br/> for <font color="Olive" title="b3">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b3">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">k</font>)</span>)</span>)</span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:31"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
( <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V5" title="AMISTD_5:attr.5">relocable1</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V6" title="AMISTD_5:attr.6">relocable2</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="amistd_5.html#V4" title="AMISTD_5:attr.4">CurIns-recognized</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</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">q</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">p</font> holds <br/> for <font color="Olive" title="b3">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b3">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">k</font>)</span>)</span>)</span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">q</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">p</font> holds <br/> for <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b2">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">k</font>)</span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c3">q</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</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#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> implies  for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Olive" title="b1">k</font>)</span>)</span>)</span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E2:31"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font>
 ; <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">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Olive" title="b1">k</font>)</span>)</span>)</span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <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#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">p</font>)</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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E4:31"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T141" title="PBOOLE:th.141">PBOOLE:141</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E6:31"/><span class="lab"><font color="Green" title="E21">C4</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T145" title="PBOOLE:th.145">PBOOLE:145</a></span>;<br/>
<a NAME="E7:31"/><span class="lab"><font color="Green" title="E22">B4</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>;<br/>
<a NAME="E8:31"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
(  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>) is  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>) <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a>  &amp;  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>) is  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>) <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="amistd_5.html#T12" target="_self" title="AMISTD_5:th.12">Th12</a>, <a class="ref" href="amistd_5.html#T11" target="_self" title="AMISTD_5:th.11">Th11</a>, <a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<a NAME="E9:31"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>) is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:31"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>;<br/>
<a NAME="E10:31"/>
<font color="Maroon" title="c7">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:31"><span class="lab"><font color="Green" title="E22">B4</font></span></a>, <a class="txt" href="#E6:31"><span class="lab"><font color="Green" title="E21">C4</font></span></a>, <a class="ref" href="extpro_1.html#D11" title="EXTPRO_1:def.11">EXTPRO_1:def 11</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">j1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E12:31"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c8">j1</font>)
 <span class="kw">and </span><br/><a NAME="E13:31"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c7">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#D9" title="EXTPRO_1:def.9">EXTPRO_1:def 9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">t</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E15:31"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T141" title="PBOOLE:th.141">PBOOLE:141</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">Q</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E17:31"/><span class="lab"><font color="Green" title="E28">C10</font></span>: 
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T145" title="PBOOLE:th.145">PBOOLE:145</a></span>;<br/>
<a NAME="E18:31"/><span class="lab"><font color="Green" title="E29">B10</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:31"><span class="lab"><font color="Green" title="E27">A10</font></span></a></span>;<br/>
<font color="Maroon" title="c10">Q</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c8">j1</font>)</span>)</span></span>)</span> = 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c10">Q</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c8">j1</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>
<br/>.= 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c7">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c8">j1</font>)</span>)</span>)</span>)</span>,<font color="Maroon" title="c5">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="amistd_5.html#D5" target="_self" title="AMISTD_5:def.5">Def5</a>, <a class="txt" href="#E6:31"><span class="lab"><font color="Green" title="E21">C4</font></span></a>, <a class="txt" href="#E17:31"><span class="lab"><font color="Green" title="E28">C10</font></span></a>, <a class="txt" href="#E7:31"><span class="lab"><font color="Green" title="E22">B4</font></span></a>, <a class="txt" href="#E18:31"><span class="lab"><font color="Green" title="E29">B10</font></span></a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:31"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E13:31"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
;<br/>
<a NAME="E20:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A12</font></span>: 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c8">j1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T7" title="EXTPRO_1:th.7">EXTPRO_1:7</a></span>;<br/>
<a NAME="E21:31"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>,<font color="Maroon" title="c8">j1</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c8">j1</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="amistd_5.html#D6" target="_self" title="AMISTD_5:def.6">Def6</a>, <a class="txt" href="#E17:31"><span class="lab"><font color="Green" title="E28">C10</font></span></a>, <a class="txt" href="#E6:31"><span class="lab"><font color="Green" title="E21">C4</font></span></a>, <a class="txt" href="#E18:31"><span class="lab"><font color="Green" title="E29">B10</font></span></a>, <a class="txt" href="#E7:31"><span class="lab"><font color="Green" title="E22">B4</font></span></a></span>;<br/>
<a NAME="E22:31"/><span class="lab"><font color="Green" title="E32">DPDP</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c4">p</font> <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="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T51" title="MEMSTR_0:th.51">MEMSTR_0:51</a></span>;<br/>
<a NAME="E23:31"/><span class="lab"><font color="Green" title="E33">aa</font></span>: 
<font color="Maroon" title="c4">p</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>;<br/>
<span class="kw">thus </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#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">p</font>)</span>)</span> = 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E6:31"><span class="lab"><font color="Green" title="E21">C4</font></span></a>, <a class="txt" href="#E23:31"><span class="lab"><font color="Green" title="E33">aa</font></span></a>, <a class="ref" href="extpro_1.html#D13" title="EXTPRO_1:def.13">EXTPRO_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T14" title="MEMSTR_0:th.14">MEMSTR_0:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:31"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E21:31"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E22:31"><span class="lab"><font color="Green" title="E32">DPDP</font></span></a>, <a class="ref" href="memstr_0.html#T14" title="MEMSTR_0:th.14">MEMSTR_0:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c10">Q</font>,<font color="Maroon" title="c9">t</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>)</span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<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#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:31"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E17:31"><span class="lab"><font color="Green" title="E28">C10</font></span></a>, <a class="txt" href="#E18:31"><span class="lab"><font color="Green" title="E29">B10</font></span></a>, <a class="ref" href="extpro_1.html#D13" title="EXTPRO_1:def.13">EXTPRO_1:def 13</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>
