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<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</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="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="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="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="memstr_0.html#K3" title="MEMSTR_0:func.3">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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="b2">a</font>,<font color="Olive" title="b1">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b3">s</font></span>)</span>,<font color="Olive" title="b5">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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">k</font></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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">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="b4">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="b2">a</font>,<font color="Olive" title="b1">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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#K2" title="NAT_1:func.2">+</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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="b2">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">k</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">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">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="firebrick">::  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="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="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="memstr_0.html#K3" title="MEMSTR_0:func.3">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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b2">s</font></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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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> &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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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#K2" title="NAT_1:func.2">+</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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<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="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="Maroon" title="c1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">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></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">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="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="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="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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#K2" title="NAT_1:func.2">+</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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">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></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">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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> &amp; <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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></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="c5">k</font>, <font color="Maroon" title="c6">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="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c6">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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="c7">D</font> =  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">s1</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">P1</font> = <font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s0k</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">s2</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">s3</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:20"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="firebrick">::  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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c6">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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">assume </span><a NAME="E2:20"/><span class="lab"><font color="Green" title="E13">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c6">n</font>)
 ; <a class="txt" 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"><span class="p2">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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">assume </span><a NAME="E3:20"/><span class="lab"><font color="Green" title="E14">A7</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="firebrick">::  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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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">thus </span> <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></span>)</span> = 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="scmfsa6a.html#T37" title="SCMFSA6A:th.37">SCMFSA6A:37</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmisort.html#K1" title="SCMISORT:func.1">StepWhile&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">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="c5">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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></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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</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="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">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="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="c1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <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="c3">a</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c5">k</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="#E2:20"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
