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<span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/>  for <font color="Olive" title="b2">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a><br/>  for <font color="Olive" title="b3">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b4">k</font>, <font color="Olive" title="b5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b3">s</font></span>)</span>,<font color="Olive" title="b5">n</font>) holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a><br/>  for <font color="Olive" title="b2">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b2">s</font></span>)</span>,<font color="Olive" title="b4">n</font>) holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b2">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b3">n</font>) holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Olive" title="b2">n</font>) holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">k</font>, <font color="Maroon" title="c7">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c7">n</font>) implies ( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) ) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c8">D</font> = <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">s1</font> =  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">P1</font> = <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">sk</font> = <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">s2</font> =  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c7">n</font>) or ( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:50"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c7">n</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</span><br/>

<a NAME="E3:50"/>
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font> is  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/>
<a NAME="E4:50"/><span class="kw">then </span>
 <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">Start-At</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T29" onmouseover="rs('memstr_0/T29')" onmouseout="rh()">MEMSTR_0:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:50"/>
 <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T98" onmouseover="rs('funct_4/T98')" onmouseout="rh()">FUNCT_4:98</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>)</span><br/>

<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</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"><span class="p4">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D2" target="_self" onmouseover="rs('scmfsa_9/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <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"><span class="p5">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="extpro_1.html#T4" onmouseover="rs('extpro_1/T4')" onmouseout="rh()">EXTPRO_1:4</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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