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<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#V4" title="AMISTD_5:attr.4">CurIns-recognized</a>  &amp; <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="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>  holds <br/> for <font color="Olive" title="b2">F</font> being   <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">data-only</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Olive" title="b1">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Olive" title="b1">S</font></span>)</span><br/>  for <font color="Olive" title="b3">l</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> <br/>  for <font color="Olive" title="b4">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="b5">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>4</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>4</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="b5">p</font> holds <br/> for <font color="Olive" title="b6">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 <br/> ( <font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b2">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b6">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b2">F</font> )</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#V4" title="AMISTD_5:attr.4">CurIns-recognized</a>  &amp; <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="compos_1.html#V10" title="COMPOS_1:attr.10">proper-halt</a>  implies  for <font color="Olive" title="b1">F</font> being   <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">data-only</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span><br/>  for <font color="Olive" title="b2">l</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> <br/>  for <font color="Olive" title="b3">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="b4">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>3</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>3</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="b4">p</font> holds <br/> for <font color="Olive" title="b5">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 <br/> ( <font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b5">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:33"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
( <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="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="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">F</font> being   <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">data-only</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span><br/>  for <font color="Olive" title="b2">l</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> <br/>  for <font color="Olive" title="b3">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="b4">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>3</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Olive">b<sub>3</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="b4">p</font> holds <br/> for <font color="Olive" title="b5">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 <br/> ( <font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b5">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">data-only</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font></span>)</span>; <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">l</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> <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="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="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="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="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 <br/> ( <font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <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>), <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>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">l</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">  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 <br/> ( <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <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>), <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>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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="c5">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c5">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 <br/> ( <font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b2">k</font>), <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>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">p</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c5">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c5">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="c6">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 <br/> ( <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Olive" title="b1">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E2:33"/><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="c6">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 <br/> ( <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Olive" title="b1">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">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"> ( <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> iff  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> implies <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:33_1"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font></span><br/><span class="kw">thus </span><a NAME="E2:33_1"/>
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D14" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c3">F</font> or  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></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="c5">q</font>,<font color="Maroon" title="c7">k</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:33_1_1"/><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c8">x</font> <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="c3">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></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="c5">q</font>,<font color="Maroon" title="c7">k</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">d1</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E3:33_1_1"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d1</font>
 <span class="kw">and </span><br/><a NAME="E4:33_1_1"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font>
 <span class="kw">and </span><br/><a NAME="E5:33_1_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="extpro_1.html#D14" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a></span>;<br/>
<a NAME="E6:33_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">d</font> = <font color="Maroon" title="c8">x</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="memstr_0.html#T76" title="MEMSTR_0:th.76">MEMSTR_0:76</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">d</font> = <font color="Maroon" title="c10">d</font> as   <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">data-only</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="memstr_0.html#D14" title="MEMSTR_0:def.14">MEMSTR_0:def 14</a></span>;<br/>
<a NAME="E9:33_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c11">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E10:33_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A10</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> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E11:33_1_1"/><span class="lab"><font color="Green" title="E26">A17</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is <font color="Maroon" title="c5">q</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="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E4:33_1_1"><span class="lab"><font color="Green" title="E23">A8</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="E12:33_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A18</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>) is  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">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="#E10:33_1_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="amistd_5.html#T11" target="_self" title="AMISTD_5:th.11">Th11</a>, <a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<a NAME="E13:33_1_1"/><span class="lab"><font color="Green" title="E28">A19</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is <font color="Maroon" title="c5">q</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E4:33_1_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">pd</font> = <font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c5">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c5">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E4:33_1_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>;<br/>
<span class="lab"><font color="Green" title="E29">A20</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#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c12">pd</font>)</span>)</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E10:33_1_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="amistd_5.html#T13" target="_self" title="AMISTD_5:th.13">Th13</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="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T54" title="MEMSTR_0:th.54">MEMSTR_0:54</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">Fs1</font> = <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33_1_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">d</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="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">d</font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</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="c5">q</font>,<font color="Maroon" title="c7">k</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E17:33_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</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="c5">q</font>,<font color="Maroon" title="c7">k</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>) )</span><br/>

<a NAME="E18:33_1_1"/>
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T54" title="MEMSTR_0:th.54">MEMSTR_0:54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:33_1_1"/>
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</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="c5">q</font>,<font color="Maroon" title="c7">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:33_1_1"><span class="lab"><font color="Green" title="E26">A17</font></span></a>, <a class="txt" href="#E13:33_1_1"><span class="lab"><font color="Green" title="E28">A19</font></span></a>, <a class="txt" href="#E12:33_1_1"><span class="lab"><font color="Green" title="E27">A18</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>; <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="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span><br/>

<a NAME="E20:33_1_1"/><span class="lab"><font color="Green" title="E30">SS</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">pd</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a></span>;<br/>
<a NAME="E21:33_1_1"/><span class="lab"><font color="Green" title="E31">A21</font></span>: 
<font color="Maroon" title="c13">Fs1</font> is  <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">data-only</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="memstr_0.html#D14" title="MEMSTR_0:def.14">MEMSTR_0:def 14</a></span>;<br/>
<a NAME="E22:33_1_1"/>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33_1_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E21:33_1_1"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E20:33_1_1"><span class="lab"><font color="Green" title="E30">SS</font></span></a>, <a class="txt" href="#E15:33_1_1"><span class="lab"><font color="Green" title="E29">A20</font></span></a>, <a class="ref" href="memstr_0.html#T5" title="MEMSTR_0:th.5">MEMSTR_0:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:33_1_1"/>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E21:33_1_1"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="ref" href="memstr_0.html#T5" title="MEMSTR_0:th.5">MEMSTR_0:5</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><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E4:33"/><span class="lab"><font color="Green" title="E20">A22</font></span>: 
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>), <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</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="c5">q</font>,<font color="Maroon" title="c6">p</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <font color="Maroon" title="c3">F</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D14" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c3">F</font> or  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) ) )</span><br/>

<span class="kw">assume </span><a NAME="E5:33"/><span class="lab"><font color="Green" title="E21">A23</font></span>: 
<font color="Maroon" title="c8">x</font> <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="c3">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">d1</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E7:33"/><span class="lab"><font color="Green" title="E22">A24</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">d1</font>
 <span class="kw">and </span><br/><a NAME="E8:33"/><span class="lab"><font color="Green" title="E23">A25</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</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="c5">q</font>,<font color="Maroon" title="c7">k</font>)
 <span class="kw">and </span><br/><a NAME="E9:33"/><span class="lab"><font color="Green" title="E24">A26</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33"><span class="lab"><font color="Green" title="E20">A22</font></span></a>, <a class="ref" href="extpro_1.html#D14" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a></span>;<br/>
<a NAME="E10:33"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">FinPartSt</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">d</font> = <font color="Maroon" title="c8">x</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33"><span class="lab"><font color="Green" title="E21">A23</font></span></a>, <a class="ref" href="memstr_0.html#T76" title="MEMSTR_0:th.76">MEMSTR_0:76</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">d</font> = <font color="Maroon" title="c10">d</font> as   <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">data-only</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33"><span class="lab"><font color="Green" title="E21">A23</font></span></a>, <a class="ref" href="memstr_0.html#D14" title="MEMSTR_0:def.14">MEMSTR_0:def 14</a></span>;<br/>
<a NAME="E13:33"/><span class="lab"><font color="Green" title="E25">B27</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c11">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E14:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A27</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> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E15:33"/><span class="lab"><font color="Green" title="E27">A32</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T54" title="MEMSTR_0:th.54">MEMSTR_0:54</a></span>;<br/>
<a NAME="E16:33"/>
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>) is  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">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="#E7:33"><span class="lab"><font color="Green" title="E22">A24</font></span></a>, <a class="txt" href="#E8:33"><span class="lab"><font color="Green" title="E23">A25</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E27">A32</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="E17:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A33</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is <font color="Maroon" title="c5">q</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="#E14:33"><span class="lab"><font color="Green" title="E26">A27</font></span></a>, <a class="ref" href="amistd_5.html#T11" target="_self" title="AMISTD_5:th.11">Th11</a>, <a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<a NAME="E18:33"/><span class="lab"><font color="Green" title="E29">RR</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>) is  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>) <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E22">A24</font></span></a>, <a class="txt" href="#E8:33"><span class="lab"><font color="Green" title="E23">A25</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E27">A32</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="E19:33"/><span class="lab"><font color="Green" title="E30">A34</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is <font color="Maroon" title="c5">q</font> <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:33"><span class="lab"><font color="Green" title="E26">A27</font></span></a>, <a class="ref" href="amistd_5.html#T12" target="_self" title="AMISTD_5:th.12">Th12</a>, <a class="txt" href="#E17:33"><span class="lab"><font color="Green" title="E28">A33</font></span></a>, <a class="txt" href="#E18:33"><span class="lab"><font color="Green" title="E29">RR</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">pd</font> = <font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c5">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <font color="Maroon" title="c5">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:33"><span class="lab"><font color="Green" title="E26">A27</font></span></a>, <a class="ref" href="amistd_5.html#T12" target="_self" title="AMISTD_5:th.12">Th12</a>, <a class="txt" href="#E17:33"><span class="lab"><font color="Green" title="E28">A33</font></span></a>, <a class="txt" href="#E18:33"><span class="lab"><font color="Green" title="E29">RR</font></span></a></span>;<br/>
<a NAME="E21:33"/><span class="lab"><font color="Green" title="E31">WR</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="c12">pd</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E25">B27</font></span></a>, <a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="lab"><font color="Green" title="E32">A35</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#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="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">k</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c9">d1</font></span>)</span>)</span>)</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> (<span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">k</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>,<font color="Maroon" title="c7">k</font>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E22">A24</font></span></a>, <a class="ref" href="memstr_0.html#T54" title="MEMSTR_0:th.54">MEMSTR_0:54</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> (<font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_5.html#T13" target="_self" title="AMISTD_5:th.13">Th13</a>, <a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E21:33"><span class="lab"><font color="Green" title="E31">WR</font></span></a></span>
;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">d</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="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">d</font> &amp; <font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E23:33"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">d</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="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E24:33"/>
<font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:33"><span class="lab"><font color="Green" title="E28">A33</font></span></a>, <a class="txt" href="#E19:33"><span class="lab"><font color="Green" title="E30">A34</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>; <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="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c13">Fs1</font> = <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E24">A26</font></span></a></span>;<br/>
<a NAME="E26:33"/><span class="lab"><font color="Green" title="E33">A37</font></span>: 
<font color="Maroon" title="c13">Fs1</font> is  <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">data-only</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33"><span class="lab"><font color="Green" title="E21">A23</font></span></a>, <a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E22">A24</font></span></a>, <a class="ref" href="memstr_0.html#D14" title="MEMSTR_0:def.14">MEMSTR_0:def 14</a></span>;<br/>
<a NAME="E27:33"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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> (<font color="Maroon" title="c5">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:33"><span class="lab"><font color="Green" title="E32">A35</font></span></a>, <a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E24">A26</font></span></a>, <a class="ref" href="memstr_0.html#T5" title="MEMSTR_0:th.5">MEMSTR_0:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E28:33"/>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c5">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">d</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E22">A24</font></span></a>, <a class="txt" href="#E26:33"><span class="lab"><font color="Green" title="E33">A37</font></span></a>, <a class="ref" href="memstr_0.html#T5" title="MEMSTR_0:th.5">MEMSTR_0:5</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>
