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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="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>  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> <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="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="b4">p</font> being  <font color="Olive">b<sub>3</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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="b4">p</font> holds <br/> for <font color="Olive" title="b5">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Olive" title="b1">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">s</font> holds <br/> for <font color="Olive" title="b6">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Olive" title="b1">S</font>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b2">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">P</font> holds <br/> for <font color="Olive" title="b7">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b6">P</font>,<font color="Olive" title="b5">s</font>,<font color="Olive" title="b7">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b6">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b3">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b5">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b4">p</font></span>)</span>,<font color="Olive" title="b7">i</font>)</span>)</span>,<font color="Olive" title="b2">k</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="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>  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> <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  <font color="Olive">b<sub>2</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">s</font> holds <br/> for <font color="Olive" title="b5">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">P</font> holds <br/> for <font color="Olive" title="b6">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b4">s</font>,<font color="Olive" title="b6">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b5">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b3">p</font></span>)</span>,<font color="Olive" title="b6">i</font>)</span>)</span>,<font color="Olive" title="b1">k</font>) )</span><br/>



<span class="kw">assume </span><a NAME="E1:23"/><span class="lab"><font color="Green" title="E11">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> 
 ; <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> <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  <font color="Olive">b<sub>2</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">s</font> holds <br/> for <font color="Olive" title="b5">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">P</font> holds <br/> for <font color="Olive" title="b6">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b4">s</font>,<font color="Olive" title="b6">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b5">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b3">p</font></span>)</span>,<font color="Olive" title="b6">i</font>)</span>)</span>,<font color="Olive" title="b1">k</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">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">  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  <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s</font> holds <br/> for <font color="Olive" title="b4">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">P</font> holds <br/> for <font color="Olive" title="b5">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b4">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b5">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b4">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">p</font></span>)</span>,<font color="Olive" title="b5">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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  <font color="Maroon" title="c4">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s</font> holds <br/> for <font color="Olive" title="b3">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">P</font> holds <br/> for <font color="Olive" title="b4">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b3">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Olive" title="b4">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">p</font> be  <font color="Maroon" title="c4">q</font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</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="c5">p</font> implies  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/> for <font color="Olive" title="b2">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font> holds <br/> for <font color="Olive" title="b3">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b3">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) )</span><br/>





<span class="kw">assume </span><a NAME="E2:23"/><span class="lab"><font color="Green" title="E12">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="c5">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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>  st  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/> for <font color="Olive" title="b2">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font> holds <br/> for <font color="Olive" title="b3">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b3">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span><br/>

<a NAME="E3:23"/><span class="lab"><font color="Green" title="E13">B2</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="c5">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E12">A2</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</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#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font> implies  for <font color="Olive" title="b1">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> holds <br/> for <font color="Olive" title="b2">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive" title="b2">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b2">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E4:23"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</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">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>  st  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> holds <br/> for <font color="Olive" title="b2">i</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive" title="b2">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b2">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</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="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> implies  for <font color="Olive" title="b1">i</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="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="Olive" title="b1">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E5:23"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">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">i</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="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="Olive" title="b1">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Olive" title="b1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <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">means </span> <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>,$1) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,$1)</span>)</span>,<font color="Maroon" title="c3">k</font>);<br/>
<a NAME="E6:23"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 for <font color="Olive" title="b1">i</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>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">i</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">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:23_1"/><span class="lab"><font color="Green" title="E17">A7</font></span>: 
 <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">i</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</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">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">kk</font> =  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span> as    <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/>
<a NAME="E3:23_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E4:23_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A8</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"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:23_1"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E6:23_1"/><span class="lab"><font color="Green" title="E20">A11</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E7:23_1"/>
 not <font color="Maroon" title="c5">p</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E12">A2</font></span></a></span>;<br/>
<a NAME="E8:23_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A12</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span> <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">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="amistd_5.html#D4" target="_self" title="AMISTD_5:def.4">Def4</a>, <a class="txt" href="#E5:23_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E6:23_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a></span>;<br/>
<a NAME="E9:23_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A13</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span> <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"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>;<br/>
<a NAME="E10:23_1"/><span class="lab"><font color="Green" title="E23">A14</font></span>: 
<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> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="compos_1.html#T46" title="COMPOS_1:th.46">COMPOS_1:46</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">kk</font> =  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span> as    <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/>
<span class="lab"><font color="Green" title="E24">A15</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</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">i</font>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</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">i</font>)</span>)</span>

<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1"><span class="lab"><font color="Green" title="E17">A7</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_1"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
<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> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
;<br/>
<a NAME="E13:23_1"/><span class="lab"><font color="Green" title="E25">A16</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E14:23_1"/><span class="lab"><font color="Green" title="E26">A17</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">kk</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E15:23_1"/><span class="lab"><font color="Green" title="E27">A18</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="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E16:23_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E28">A19</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#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">i</font>)</span>)</span>) = 
<font color="Maroon" title="c7">P</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="c7">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c7">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E10:23_1"><span class="lab"><font color="Green" title="E23">A14</font></span></a>, <a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23_1"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="ref" href="compos_1.html#T34" title="COMPOS_1:th.34">COMPOS_1:34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">IncAddr</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">kk</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23_1"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="valued_1.html#D12" title="VALUED_1:def.12">VALUED_1:def 12</a></span>
<br/>.= 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">kk</font></span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="compos_1.html#D19" title="COMPOS_1:def.19">COMPOS_1:def 19</a></span>
<br/>.= 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="txt" href="#E14:23_1"><span class="lab"><font color="Green" title="E26">A17</font></span></a>, <a class="txt" href="#E13:23_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</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> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>)</span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:23_1"><span class="lab"><font color="Green" title="E27">A18</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
;<br/>
<span class="kw">thus </span> <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>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c7">P</font>,<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">i</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p2">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23_1"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E17:23_1"><span class="lab"><font color="Green" title="E28">A19</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c8">i</font>)</span>)</span>)</span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_5.html#T4" target="_self" title="AMISTD_5:th.4">Th4</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</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>
<span class="kw">set </span><font color="Maroon" title="c8">IP</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c2">S</font>);<br/>
<a NAME="E7:23"/><span class="lab"><font color="Green" title="E17">A21</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E8:23"/><span class="lab"><font color="Green" title="E18">B22</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T55" title="MEMSTR_0:th.55">MEMSTR_0:55</a></span>;<br/>
<span class="lab"><font color="Green" title="E19">B23</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E13">B2</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font>

;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">DP</font> =  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c5">p</font>;<br/>
<a NAME="E10:23"/>
 <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="c5">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T59" title="RELAT_1:th.59">RELAT_1:59</a></span>;<br/>
<a NAME="E11:23"/><span class="kw">then </span>
 <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="c5">p</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <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="#E4:23"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E12:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A29</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c5">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="memstr_0.html#T51" title="MEMSTR_0:th.51">MEMSTR_0:51</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">PR</font> =  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">k</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">IS</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>);<br/>
<a NAME="E13:23"/><span class="lab"><font color="Green" title="E21">A30</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
 <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>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) = 
<font color="Maroon" title="c6">s</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E19">B23</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E18">B22</font></span></a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E20">A29</font></span></a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c5">p</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E21">A30</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E17">A21</font></span></a>, <a class="ref" href="funct_4.html#T74" title="FUNCT_4:th.74">FUNCT_4:74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p4">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c5">p</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c2">S</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="memstr_0.html#T26" title="MEMSTR_0:th.26">MEMSTR_0:26</a></span>
<br/>.= 
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">p</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
;<br/>
<a NAME="E15:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A31</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<span class="kw">thus </span><a NAME="E16:23"/>
 for <font color="Olive" title="b1">i</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  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E22">A31</font></span></a>, <a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E16">A6</font></span></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>
