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<span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>   <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b2">J</font> being   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b3">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Olive" title="b1">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Olive" title="b2">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s</font> holds <br/>(  <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="c2">P</font>,<font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b2">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b3">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<font color="Olive" title="b3">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Olive" title="b2">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">D</font> =  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>   <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of ; <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">J</font> being   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <br/>  for <font color="Olive" title="b2">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Olive" title="b1">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s</font> holds <br/>(  <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="c2">P</font>,<font color="Olive" title="b2">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Olive" title="b1">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b2">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b2">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Olive" title="b1">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">J</font> be   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/>(  <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="c2">P</font>,<font color="Olive" title="b1">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Olive" title="b1">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</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 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font> implies (  <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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) ) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c7">s3</font> = <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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">m1</font> =  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">m3</font> =  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>);<br/>
<a NAME="E1:22"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T99" title="FUNCT_4:th.99">FUNCT_4:99</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:22"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 <span class="kw">and </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <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"> (  <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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<a NAME="E4:22"/><span class="lab"><font color="Green" title="E17">B5</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span>
 
<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="E5:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A5</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>) <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="#E3:22"><span class="lab"><font color="Green" title="E16">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="E6:22"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T16" title="SCMFSA6A:th.16">SCMFSA6A:16</a></span>;<br/>
<a NAME="E7:22"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A3</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/>
<a NAME="E8:22"/><span class="lab"><font color="Green" title="E21">A11</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/>
<a NAME="E9:22"/><span class="lab"><font color="Green" title="E22">C13</font></span>: 
<font color="Maroon" title="c6">s</font> is   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="memstr_0.html#T29" title="MEMSTR_0:th.29">MEMSTR_0:29</a></span>;<br/>
<a NAME="E10:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A14</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T1" target="_self" title="SCMFSA6B:th.1">Th18</a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:22"/><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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T13" target="_self" title="SCMFSA6B:th.13">Th37</a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E22">C13</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<div><span class="lab"><font color="Green" title="E25">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">x</font> be    <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"> ( <font color="Maroon" title="c10">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> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E26">DD</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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></span>;<br/><span class="kw">assume </span><a NAME="E2:22_1"/><span class="lab"><font color="Green" title="E27">Z</font></span>: 
<font color="Maroon" title="c10">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> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
 ; <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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E3:22_1"/><span class="lab"><font color="Green" title="E28">A20</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E27">Z</font></span></a>, <a class="ref" href="relat_1.html#T57" title="RELAT_1:th.57">RELAT_1:57</a></span>;<br/><a NAME="E4:22_1"/><span class="lab"><font color="Green" title="E29">II</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</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/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:22_1_1"/>
( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E27">Z</font></span></a>, <a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E26">DD</font></span></a>, <a class="ref" href="scmfsa6a.html#T42" title="SCMFSA6A:th.42">SCMFSA6A:42</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_1"/><span class="lab"><font color="Green" title="E30">A22</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 ; <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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:22_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">B22</font></span>: 
<font color="Maroon" title="c10">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> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T42" title="SCMFSA6A:th.42">SCMFSA6A:42</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1_1"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a>, <a class="ref" href="scmfsa6a.html#T43" title="SCMFSA6A:th.43">SCMFSA6A:43</a></span>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E2:22_1_1_1"><span class="lab"><font color="Green" title="E31">B22</font></span></a>, <a class="txt" href="#E1:22_1_1_1"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a>, <a class="ref" href="scmfsa6a.html#T43" title="SCMFSA6A:th.43">SCMFSA6A:43</a></span>
<br/>.= 
<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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1_1"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="ref" href="scmfsa6b.html#D4" target="_self" title="SCMFSA6B:def.4">Def4</a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E29">II</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E22">C13</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_1_1_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> 
 ; <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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:22_1_1_2"/><span class="kw">then </span>
 not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#T3" title="STRUCT_0:th.3">STRUCT_0:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:22_1_1_2"/>
<span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E27">Z</font></span></a>, <a class="ref" href="relat_1.html#T57" title="RELAT_1:th.57">RELAT_1:57</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></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c10">s4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E14:22"/><span class="lab"><font color="Green" title="E26">A23</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>
 
<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="E15:22"/>
<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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="E16:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A25</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="ref" href="scmfsa6b.html#T2" target="_self" title="SCMFSA6B:th.2">Th19</a></span>;<br/>
<a NAME="E17:22"/><span class="lab"><font color="Green" title="E28">B24</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 
<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/>
<a NAME="E18:22"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E19:22"/><span class="kw">then </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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:22"><span class="lab"><font color="Green" title="E28">B24</font></span></a>, <a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></span>;<br/>
<a NAME="E20:22"/><span class="kw">then </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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E21:22"/><span class="kw">then </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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<a NAME="E22:22"/><span class="kw">then </span>
(  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">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#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span> <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#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="funct_4.html#T71" title="FUNCT_4:th.71">FUNCT_4:71</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<a NAME="E23:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A26</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/>
<a NAME="E24:22"/>
<font color="Maroon" title="c6">s</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E17">B5</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E16">A4</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/>
<a NAME="E25:22"/><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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:22"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="ref" href="scmfsa6b.html#T16" target="_self" title="SCMFSA6B:th.16">Th40</a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E23">A14</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:22"/><span class="lab"><font color="Green" title="E30">A28</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E23">A14</font></span></a>, <a class="ref" href="scmfsa6b.html#T14" target="_self" title="SCMFSA6B:th.14">Th38</a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E22">C13</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></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">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<a NAME="E27:22"/>
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c5">J</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/>
<span class="kw">hence </span><a NAME="E28:22"/><span class="lab"><font color="Green" title="E31">A31</font></span>: 
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Reloc</a> (<font color="Maroon" title="c5">J</font>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<a NAME="E29:22"/>
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T2" title="SCMFSA_2:th.2">SCMFSA_2:2</a></span>;<br/>
<a NAME="E30:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A33</font></span>: 
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T100" title="SCMFSA_2:th.100">SCMFSA_2:100</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:22"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a>, <a class="ref" href="scmfsa6a.html#T41" title="SCMFSA6A:th.41">SCMFSA6A:41</a>, <a class="ref" href="scmfsa6a.html#T43" title="SCMFSA6A:th.43">SCMFSA6A:43</a></span>
;<br/> <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">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font> &amp;  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<a NAME="E32:22"/><span class="lab"><font color="Green" title="E33">A34</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/>
<a NAME="E33:22"/><span class="lab"><font color="Green" title="E34">A36</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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="E34:22"/><span class="kw">then </span>
 <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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p0">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="scmfsa6b.html#T6" target="_self" title="SCMFSA6B:th.6">Th27</a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E31">A31</font></span></a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E35">A37</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c11">m</font>)</span>)</span>) = 
 <a href="compos_1.html#K9" title="COMPOS_1:func.9">IncAddr</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:22"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E32:22"><span class="lab"><font color="Green" title="E33">A34</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T11" title="COMPOS_1:th.11">COMPOS_1:11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E36:22"/><span class="lab"><font color="Green" title="E36">A38</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span> &amp; ( <font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</span><br/>

<div><span class="lab"><font color="Green" title="E37">A39</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">m</font> implies  not  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">k</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )</span><br/><span class="kw">assume </span><a NAME="E1:22_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">k</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><a NAME="E2:22_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A40</font></span>: 
<font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><span class="kw">assume </span><a NAME="E3:22_4"/><span class="lab"><font color="Green" title="E39">A41</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">k</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span>) = 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="scmfsa6b.html#T6" target="_self" title="SCMFSA6B:th.6">Th27</a>, <a class="txt" href="#E33:22"><span class="lab"><font color="Green" title="E34">A36</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E31">A31</font></span></a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_4"><span class="lab"><font color="Green" title="E39">A41</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/><a NAME="E5:22_4"/><span class="kw">then </span>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D17" title="COMPOS_1:def.17">COMPOS_1:def 17</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>;<br/><a NAME="E6:22_4"/><span class="kw">then </span>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></span>;<br/><span class="kw">hence </span><a NAME="E7:22_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:22"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E2:22_4"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="c12">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">m</font> implies  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )</span><br/><span class="kw">assume </span><a NAME="E1:22_5"/><span class="lab"><font color="Green" title="E38">A42</font></span>: 
<font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_5_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:22_5_1"/>
( <font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>) or  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_5_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_5_1_1"/><span class="lab"><font color="Green" title="E39">A43</font></span>: 
<font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<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">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><a NAME="E2:22_5_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c4">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="funct_4.html#T74" title="FUNCT_4:th.74">FUNCT_4:74</a></span>;<br/><span class="kw">hence </span><a NAME="E3:22_5_1_1"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c12">k</font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="scmfsa6b.html#T15" target="_self" title="SCMFSA6B:th.15">Th39</a>, <a class="txt" href="#E1:22_5_1_1"><span class="lab"><font color="Green" title="E39">A43</font></span></a>, <a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_5_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_5_1_2"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span><br/><div class="add"><a NAME="E2:22_5_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">kk</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E4:22_5_1_2"/><span class="lab"><font color="Green" title="E39">A44</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c13">kk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><a NAME="E5:22_5_1_2"/>
<font color="Maroon" title="c13">kk</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><span class="kw">hence </span><a NAME="E6:22_5_1_2"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c12">k</font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:22_5"><span class="lab"><font color="Green" title="E38">A42</font></span></a>, <a class="txt" href="#E4:22_5_1_2"><span class="lab"><font color="Green" title="E39">A44</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><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E39:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A45</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">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="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">k</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds <br/><font color="Maroon" title="c11">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 
;<br/>
<a NAME="E40:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A46</font></span>: 
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:22"><span class="lab"><font color="Green" title="E35">A37</font></span></a>, <a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E36">A38</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>;<br/>
<a NAME="E41:22"/>
<font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c6">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T2" target="_self" title="SCMFSA6B:th.2">Th19</a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E42:22"/><span class="kw">then </span>
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E43:22"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E38">A45</font></span></a>, <a class="txt" href="#E35:22"><span class="lab"><font color="Green" title="E35">A37</font></span></a>, <a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E36">A38</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</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="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>  implies <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</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"> verum</span>
<div class="add"><a NAME="E1:22_6"/><span class="lab"><font color="Green" title="E40">A50</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="scmfsa6b.html#T6" target="_self" title="SCMFSA6B:th.6">Th27</a>, <a class="txt" href="#E33:22"><span class="lab"><font color="Green" title="E34">A36</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E31">A31</font></span></a></span>;<br/><a NAME="E2:22_6"/><span class="lab"><font color="Green" title="E41">IJ</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</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/><span class="kw">assume </span><a NAME="E3:22_6"/><span class="lab"><font color="Green" title="E42">A51</font></span>: 
<font color="Maroon" title="c5">J</font> is  <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a> 
 ; <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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c11">m</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E36">A38</font></span></a>, <a class="txt" href="#E40:22"><span class="lab"><font color="Green" title="E39">A46</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p2">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">J</font></span>)</span>,<span class="p3">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_6"><span class="lab"><font color="Green" title="E40">A50</font></span></a>, <a class="ref" href="scmfsa6a.html#T7" title="SCMFSA6A:th.7">SCMFSA6A:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">I</font></span>)</span>,<font color="Maroon" title="c6">s</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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_6"><span class="lab"><font color="Green" title="E42">A51</font></span></a>, <a class="ref" href="scmfsa6b.html#D4" target="_self" title="SCMFSA6B:def.4">Def4</a>, <a class="txt" href="#E2:22_6"><span class="lab"><font color="Green" title="E41">IJ</font></span></a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a>, <a class="ref" href="scmfsa6a.html#T41" title="SCMFSA6A:th.41">SCMFSA6A:41</a>, <a class="ref" href="scmfsa6a.html#T43" title="SCMFSA6A:th.43">SCMFSA6A:43</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>
