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<span class="kw">let </span><font color="Maroon" title="c3">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="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#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b3">J</font> being   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b4">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/>  for <font color="Olive" title="b5">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b4">a</font></span>)</span>,<font color="Olive" title="b5">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b3">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Olive" title="b3">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">k1</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Olive" title="b3">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b3">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <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" 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#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">J</font> being   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b3">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/>  for <font color="Olive" title="b4">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b3">a</font></span>)</span>,<font color="Olive" title="b4">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Olive" title="b2">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">k1</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Olive" title="b2">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">J</font> being   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/>  for <font color="Olive" title="b3">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b3">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Olive" title="b1">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Olive" title="b1">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Olive" title="b1">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">J</font> be   <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>   <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> <br/>  for <font color="Olive" title="b2">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<font color="Olive" title="b2">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Olive" title="b1">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> holds <br/> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Olive" title="b1">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">k1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> implies  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span> )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c9">b</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">pJ</font> =  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s1</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">P1</font> = <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">P2</font> = <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">IF</font> =  <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c15">pIF</font> =  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">s3</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">P3</font> = <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">s4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1);<br/>
<span class="kw">set </span><font color="Maroon" title="c19">P4</font> = <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">i</font> = (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">G</font> =  <a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">iG</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">SAl</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>);<br/>
<span class="lab"><font color="Green" title="E34">A3</font></span>:  <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c6">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T14" title="SCMPDS_4:th.14">SCMPDS_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c6">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T14" title="SCMPDS_4:th.14">SCMPDS_4:14</a></span>
;<br/>
<span class="lab"><font color="Green" title="E35">A4</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="scmpds_6.html#T11" target="_self" title="SCMPDS_6:th.11">Th22</a></span>
;<br/>
<a NAME="E3:49"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
 not  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">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" title="SCMPDS_4:th.18">SCMPDS_4:18</a></span>;<br/>
<a NAME="E4:49"/>
 not <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">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" title="SCMPDS_4:th.18">SCMPDS_4:18</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E37">A6</font></span>: <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
;<br/>
<a NAME="E6:49"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T47" title="MEMSTR_0:th.47">MEMSTR_0:47</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:49"/>
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c8">k1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> or  not <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> or  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span> )</span><br/>

<span class="kw">then </span><span class="lab"><font color="Green" title="E39">A9</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> (<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E5:49"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="ref" href="scmpds_2.html#T55" title="SCMPDS_2:th.55">SCMPDS_2:55</a></span>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:49"><span class="lab"><font color="Green" title="E38">A7</font></span></a>, <a class="ref" href="scmpds_6.html#T12" target="_self" title="SCMPDS_6:th.12">Th23</a></span>
;<br/>
<a NAME="E9:49"/>
 for <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  holds  <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="scmpds_2.html#T55" title="SCMPDS_2:th.55">SCMPDS_2:55</a></span>;<br/>
<a NAME="E10:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A11</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T8" title="SCMPDS_4:th.8">SCMPDS_4:8</a></span>;<br/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T54" title="COMPOS_1:th.54">COMPOS_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T6" target="_self" title="SCMPDS_6:th.6">Th15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

;<br/>
<a NAME="E12:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A12</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T13" target="_self" title="SCMPDS_6:th.13">Th24</a></span>;<br/>
<a NAME="E13:49"/>
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E14:49"/><span class="kw">then </span>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E15:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A13</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span>
 
;<br/>
<span class="kw">assume </span><a NAME="E16:49"/><span class="lab"><font color="Green" title="E43">A14</font></span>: 
<font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> or  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span> )</span><br/>

<a NAME="E17:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A15</font></span>: 
(  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T24" target="_self" title="SCMPDS_6:th.24">Th38</a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E18:49"/><span class="lab"><font color="Green" title="E45">UU</font></span>: 
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E19:49"/><span class="lab"><font color="Green" title="E46">A16</font></span>: 
<font color="Maroon" title="c6">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span><br/>

<a NAME="E20:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A17</font></span>: 
<font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" target="_self" title="SCMPDS_6:def.3">Def3</a></span>;<br/>
<a NAME="E21:49"/><span class="lab"><font color="Green" title="E48">A19</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/>
<span class="lab"><font color="Green" title="E49">A22</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:49"><span class="lab"><font color="Green" title="E48">A19</font></span></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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:49"><span class="lab"><font color="Green" title="E44">A15</font></span></a>, <a class="txt" href="#E15:49"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E10:49"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="ref" href="scmpds_6.html#T31" target="_self" title="SCMPDS_6:th.31">Th45</a>, <a class="txt" href="#E18:49"><span class="lab"><font color="Green" title="E45">UU</font></span></a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:49"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>
;<br/>
<a NAME="E23:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A23</font></span>: 
<font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</a></span>;<br/>
<a NAME="E24:49"/><span class="lab"><font color="Green" title="E51">A24</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>) <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="scmpds_6.html#T11" target="_self" title="SCMPDS_6:th.11">Th22</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_7"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">l</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c24">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 implies  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> )</span><br/><span class="kw">assume </span><a NAME="E1:49_7"/><span class="lab"><font color="Green" title="E52">A25</font></span>: 
<font color="Maroon" title="c24">l</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span><br/><a NAME="E2:49_7"/><span class="lab"><font color="Green" title="E53">A26</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_7_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_7_1"/>
( <font color="Maroon" title="c24">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c24">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_7_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_7_1_1"/>
<font color="Maroon" title="c24">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span><br/><div class="add"><a NAME="E2:49_7_1_1"/><span class="kw">then </span>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c24">l</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_7"><span class="lab"><font color="Green" title="E53">A26</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:49_7_1_1"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c24">l</font>)</span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:49"><span class="lab"><font color="Green" title="E51">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_7_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_7_1_2"/>
<font color="Maroon" title="c24">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive">b<sub>1</sub></font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:49_7_1_2"/><span class="lab"><font color="Green" title="E54">A27</font></span>: 
<font color="Maroon" title="c24">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">n</font> = <font color="Maroon" title="c25">n</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E5:49_7_1_2"/><span class="lab"><font color="Green" title="E55">A28</font></span>: 
<font color="Maroon" title="c26">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_7"><span class="lab"><font color="Green" title="E52">A25</font></span></a>, <a class="txt" href="#E3:49_7_1_2"><span class="lab"><font color="Green" title="E54">A27</font></span></a>, <a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><span class="kw">assume </span><a NAME="E6:49_7_1_2"/><span class="lab"><font color="Green" title="E56">A29</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c24">l</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E7:49_7_1_2"/><span class="lab"><font color="Green" title="E57">A31</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c26">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c26">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">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"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c26">n</font>)</span>)</span>) = 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c26">n</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:49"><span class="lab"><font color="Green" title="E44">A15</font></span></a>, <a class="txt" href="#E15:49"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E10:49"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="ref" href="scmpds_6.html#T31" target="_self" title="SCMPDS_6:th.31">Th45</a>, <a class="txt" href="#E18:49"><span class="lab"><font color="Green" title="E45">UU</font></span></a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_7_1_2"><span class="lab"><font color="Green" title="E54">A27</font></span></a>, <a class="txt" href="#E6:49_7_1_2"><span class="lab"><font color="Green" title="E56">A29</font></span></a>, <a class="txt" href="#E7:49_7_1_2"><span class="lab"><font color="Green" title="E57">A31</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E9:49_7_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:49"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="txt" href="#E5:49_7_1_2"><span class="lab"><font color="Green" title="E55">A28</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E26:49"/><span class="kw">then </span>
 for <font color="Olive" title="b1">l</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive" title="b1">l</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> holds <br/><span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">l</font>
 
;<br/>
<a NAME="E27:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A34</font></span>: 
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:49"><span class="lab"><font color="Green" title="E49">A22</font></span></a>, <a class="txt" href="#E23:49"><span class="lab"><font color="Green" title="E50">A23</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>;<br/>
<span class="lab"><font color="Green" title="E53">A35</font></span>:  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> = 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:49"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:49"><span class="lab"><font color="Green" title="E44">A15</font></span></a>, <a class="txt" href="#E15:49"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E10:49"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="ref" href="scmpds_6.html#T31" target="_self" title="SCMPDS_6:th.31">Th45</a>, <a class="txt" href="#E18:49"><span class="lab"><font color="Green" title="E45">UU</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:49"><span class="lab"><font color="Green" title="E50">A23</font></span></a>, <a class="txt" href="#E27:49"><span class="lab"><font color="Green" title="E52">A34</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E54">A36</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_9"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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">b<sub>1</sub></font> )</span><br/><a NAME="E1:49_9"/><span class="lab"><font color="Green" title="E55">A37</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E2:49_9"/><span class="lab"><font color="Green" title="E56">A38</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_9_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_9_1"/>
( <font color="Maroon" title="c24">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_9"><span class="lab"><font color="Green" title="E56">A38</font></span></a>, <a class="ref" href="scmpds_4.html#T6" title="SCMPDS_4:th.6">SCMPDS_4:6</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_9_1_1"/><span class="lab"><font color="Green" title="E57">A39</font></span>: 
<font color="Maroon" title="c24">x</font> is    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:49_9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T43" title="SCMPDS_2:th.43">SCMPDS_2:43</a></span>;<br/><a NAME="E3:49_9_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A40</font></span>: 
 not <font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="txt" href="#E1:49_9"><span class="lab"><font color="Green" title="E55">A37</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> = 
<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>

<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:49"><span class="lab"><font color="Green" title="E53">A35</font></span></a>, <a class="txt" href="#E1:49_9_1_1"><span class="lab"><font color="Green" title="E57">A39</font></span></a>, <a class="ref" href="scmpds_4.html#T8" title="SCMPDS_4:th.8">SCMPDS_4:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_9_1_1"><span class="lab"><font color="Green" title="E58">A40</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_9_1_2"/><span class="lab"><font color="Green" title="E57">A42</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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">b<sub>1</sub></font></span><br/><div class="add"><span class="lab"><font color="Green" title="E58">A44</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>

<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:49"><span class="lab"><font color="Green" title="E43">A14</font></span></a>, <a class="txt" href="#E19:49"><span class="lab"><font color="Green" title="E46">A16</font></span></a>, <a class="ref" href="scmpds_6.html#T34" target="_self" title="SCMPDS_6:th.34">Th48</a></span>
;<br/><a NAME="E3:49_9_1_2"/><span class="lab"><font color="Green" title="E59">A46</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="txt" href="#E1:49_9"><span class="lab"><font color="Green" title="E55">A37</font></span></a>, <a class="txt" href="#E1:49_9_1_2"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> = 
<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>

<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:49"><span class="lab"><font color="Green" title="E50">A23</font></span></a>, <a class="txt" href="#E27:49"><span class="lab"><font color="Green" title="E52">A34</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">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="c3">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#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_9_1_2"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:49"><span class="lab"><font color="Green" title="E44">A15</font></span></a>, <a class="txt" href="#E15:49"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="txt" href="#E8:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E10:49"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="ref" href="scmpds_6.html#T31" target="_self" title="SCMPDS_6:th.31">Th45</a>, <a class="txt" href="#E18:49"><span class="lab"><font color="Green" title="E45">UU</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">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#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:49"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="txt" href="#E2:49_9_1_2"><span class="lab"><font color="Green" title="E58">A44</font></span></a>, <a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_9_1_2"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E3:49_9_1_2"><span class="lab"><font color="Green" title="E59">A46</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">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#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E31:49"/>
 <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</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="txt" href="#E29:49"><span class="lab"><font color="Green" title="E54">A36</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
