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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">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="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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b4">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">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="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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b3">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="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="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b2">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">k</font>, <font color="Maroon" title="c5">n</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="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies ( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">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="c7">s1</font> = <font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">sk</font> = <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">s0k</font> =  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">At0</font> = <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s2</font> = <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">s3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:30"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <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="Red">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">n</font> or  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or ( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> ) )</span><br/>

<a NAME="E2:30"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T65" title="SF_MASTR:th.65">SF_MASTR:65</a></span>;<br/>
<span class="lab"><font color="Green" title="E16">A3</font></span>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T13" title="SCMFSA8A:th.13">SCMFSA8A:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="sf_mastr.html#T66" title="SF_MASTR:th.66">SF_MASTR:66</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E4:30"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or ( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> ) )</span><br/>

<a NAME="E5:30"/><span class="kw">then </span>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<a NAME="E6:30"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A5</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T100" title="FUNCT_4:th.100">FUNCT_4:100</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:30"/><span class="lab"><font color="Green" title="E19">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> )</span><br/>

<a NAME="E8:30"/><span class="lab"><font color="Green" title="E20">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> = 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T13" title="SCMFSA8A:th.13">SCMFSA8A:13</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T11" title="SCMFSA8A:th.11">SCMFSA8A:11</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E7:30"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="scmfsa8c.html#T14" title="SCMFSA8C:th.14">SCMFSA8C:14</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E10:30"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="scmfsa_9.html#T29" title="SCMFSA_9:th.29">SCMFSA_9:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span><br/>

<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmisort.html#D1" target="_self" title="SCMISORT:def.1">Def1</a>, <a class="txt" href="#E8:30"><span class="lab"><font color="Green" title="E20">T</font></span></a></span>
<br/>.= 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
