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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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b3">J</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> holds <br/> <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b3">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span></span>)</span>,<font color="Olive" title="b4">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">I</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b3">J</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b1">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">k</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b2">J</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b2">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> holds <br/> <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Olive" title="b3">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">I</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b2">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">k</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> holds <br/> <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Olive" title="b2">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Olive" title="b1">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">k</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">J</font> be   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> holds <br/> <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c6">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> implies  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c6">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font></span>)</span>) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c7">sIsI</font> = <font color="Maroon" title="c3">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">PIPI</font> = <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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">RI</font> =  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">pJ</font> =  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">RIJ</font> =  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">PRIJ</font> = <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">pIJ</font> =  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">sIsIJ</font> = <font color="Maroon" title="c3">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">PIPIJ</font> = <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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>;<br/>
<a NAME="E1:56"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<a NAME="E2:56"/>
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<a NAME="E3:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A2</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D7" onmouseover="rs('scmpds_4/D7')" onmouseout="rh()">SCMPDS_4:def 7</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">s2</font> =  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c17">s1</font> = <span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>);<br/>
<a NAME="E4:56"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
<font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T12" target="_self" onmouseover="rs('scmpds_5/T12')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:56"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c6">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font></span>)</span>)</span><br/>

<a NAME="E6:56"/><span class="lab"><font color="Green" title="E27">A5</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="funct_4.html#T98" onmouseover="rs('funct_4/T98')" onmouseout="rh()">FUNCT_4:98</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E28">A6</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span> &amp; (  for <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> ) )</span></a><div class="add"><span class="kw">thus </span> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T113" onmouseover="rs('funct_4/T113')" onmouseout="rh()">FUNCT_4:113</a></span>
<br/>.= 
<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T113" onmouseover="rs('funct_4/T113')" onmouseout="rh()">FUNCT_4:113</a></span>
<br/>.= 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="scmpds_5.html#T26" target="_self" onmouseover="rs('scmpds_5/T26')" onmouseout="rh()">Th14</a>, <a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font></span><br/><div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c19">a</font> be   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font></span><br/><a NAME="E1:56_1_2"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
 not <font color="Maroon" title="c19">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">Start-At</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T18" onmouseover="rs('scmpds_4/T18')" onmouseout="rh()">SCMPDS_4:18</a></span>;<br/><a NAME="E2:56_1_2"/>
 not <font color="Maroon" title="c19">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T18" onmouseover="rs('scmpds_4/T18')" onmouseout="rh()">SCMPDS_4:18</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1_2"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="funct_4.html#T11" onmouseover="rs('funct_4/T11')" onmouseout="rh()">FUNCT_4:11</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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="extpro_1.html#T23" onmouseover="rs('extpro_1/T23')" onmouseout="rh()">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> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T30" target="_self" onmouseover="rs('scmpds_5/T30')" onmouseout="rh()">Th18</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span> <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,$1)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> $1</span>)</span>);<br/>
<a NAME="E8:56"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<a NAME="E9:56"/><span class="lab"><font color="Green" title="E30">A9</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c19">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c19">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c20">k1</font> = <font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">CRk</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c22">PCRk</font> = <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">CRSk</font> =  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c24">CIJk</font> =  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c25">PCIJk</font> = <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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c26">CRk1</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c27">CRSk1</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"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p5">(<span class="default"><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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p0">(<span class="default"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c28">CIJk1</font> =  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>);<br/>
<span class="kw">assume </span><a NAME="E1:56_2"/><span class="lab"><font color="Green" title="E31">A10</font></span>: 
 <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<a NAME="E2:56_2"/><span class="lab"><font color="Green" title="E32">A11</font></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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</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> (<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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></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"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</span>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_2_1"><span class="kw">proof </span></a><div class="add">

<span class="lab"><font color="Green" title="E33">A12</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></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"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="ref" href="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>
<br/>.= 
<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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T113" onmouseover="rs('funct_4/T113')" onmouseout="rh()">FUNCT_4:113</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c29">n</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<a NAME="E3:56_2_1"/><span class="lab"><font color="Green" title="E34">A13</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" onmouseover="rs('afinsq_1/T27')" onmouseout="rh()">AFINSQ_1:27</a></span>;<br/>
<a NAME="E4:56_2_1"/><span class="lab"><font color="Green" title="E35">A14</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="scmpds_4.html#D6" onmouseover="rs('scmpds_4/D6')" onmouseout="rh()">SCMPDS_4:def 6</a></span>;<br/>
<a NAME="E5:56_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>;<br/>
<a NAME="E6:56_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/>
<a NAME="E7:56_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_2_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="afinsq_1.html#T17" onmouseover="rs('afinsq_1/T17')" onmouseout="rh()">AFINSQ_1:17</a></span>;<br/>
<a NAME="E8:56_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A15</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>;<br/>
<a NAME="E9:56_2_1"/><span class="lab"><font color="Green" title="E37">A16</font></span>: 
<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>;<br/>
<a NAME="E10:56_2_1"/>
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<span class="kw">hence </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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>) = 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56_2_1"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E9:56_2_1"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56_2_1"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E3:56_2_1"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="afinsq_1.html#D3" onmouseover="rs('afinsq_1/D3')" onmouseout="rh()">AFINSQ_1:def 3</a></span>
<br/>.= 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></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"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2_1"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="txt" href="#E8:56"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="txt" href="#E8:56_2_1"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<a NAME="E3:56_2"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</span>)</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"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E31">A10</font></span></a>, <a class="ref" href="scmpds_5.html#T31" target="_self" onmouseover="rs('scmpds_5/T31')" onmouseout="rh()">Th19</a>, <a class="txt" href="#E2:56_2"><span class="lab"><font color="Green" title="E32">A11</font></span></a>, <a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<a NAME="E4:56_2"/>
 <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)
 
;<br/>
<a NAME="E5:56_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A18</font></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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></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"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c19">k</font></span>)</span>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A19</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_2_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a> holds  <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"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <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"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c29">a</font> be   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <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"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</font></span><br/><span class="kw">thus </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"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <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"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</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"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_3.html#T6" onmouseover="rs('scmpds_3/T6')" onmouseout="rh()">SCMPDS_3:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</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> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c29">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56_2"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:56_2"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="scmpds_3.html#T6" onmouseover="rs('scmpds_3/T6')" onmouseout="rh()">SCMPDS_3:6</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</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"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <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"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T113" onmouseover="rs('funct_4/T113')" onmouseout="rh()">FUNCT_4:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p4">(<span class="default"><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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c19">k</font>)</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</a></span>
;<br/>
<a NAME="E8:56_2"/><span class="kw">then </span>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</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"><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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</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> <span class="p0">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</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#K7" title="MEMSTR_0:func.7">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <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"><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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:56_2"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E3:56_2"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="ref" href="funct_4.html#T113" onmouseover="rs('funct_4/T113')" onmouseout="rh()">FUNCT_4:113</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:56_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c19">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56_2"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="scmpds_4.html#T2" onmouseover="rs('scmpds_4/T2')" onmouseout="rh()">SCMPDS_4:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<a NAME="E10:56"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:56"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="scmpds_4.html#T2" onmouseover="rs('scmpds_4/T2')" onmouseout="rh()">SCMPDS_4:2</a></span>;<br/>
<a NAME="E11:56"/>
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" onmouseover="rs('nat_1/S2')" onmouseout="rh()">NAT_1:sch 2</a>(<a class="txt" href="#E10:56"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E9:56"><span class="lab"><font color="Green" title="E30">A9</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E12:56"/>
 <a href="memstr_0.html#K9" title="MEMSTR_0:func.9">IncIC</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</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="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <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> <span class="p5">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c6">k</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">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#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> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font></span>)</span>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
