<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">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">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">k</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> <br/>  for <font color="Olive" title="b4">P</font> being   <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> holds  <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="Olive" title="b4">P</font>,<font color="Maroon" title="c1">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="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> <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="Olive" title="b4">P</font>,<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="Olive" title="b2">a</font>,<font color="Olive" title="b4">P</font>,<font color="Maroon" title="c1">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="b3">k</font></span>)</span>,<font color="Olive" title="b1">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</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">k</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> <br/>  for <font color="Olive" title="b3">P</font> being   <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> holds  <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="b3">P</font>,<font color="Maroon" title="c1">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> <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="b3">P</font>,<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="Olive" title="b1">a</font>,<font color="Olive" title="b3">P</font>,<font color="Maroon" title="c1">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>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</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">k</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> <br/>  for <font color="Olive" title="b2">P</font> being   <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> holds  <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="Olive" title="b2">P</font>,<font color="Maroon" title="c1">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> <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="Olive" title="b2">P</font>,<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="Olive" title="b2">P</font>,<font color="Maroon" title="c1">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>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c4">k</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">  for <font color="Olive" title="b1">P</font> being   <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> holds  <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="Olive" title="b1">P</font>,<font color="Maroon" title="c1">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="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> <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="Olive" title="b1">P</font>,<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="Olive" title="b1">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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"> <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="c5">P</font>,<font color="Maroon" title="c1">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="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> <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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">sk0</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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<a NAME="E1:18"/>
<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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <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="c3">a</font>,<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font>
 
<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/>
<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">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="c5">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> <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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></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="c5">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="c5">P</font>,<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="c3">a</font>,<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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/>.= 
<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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<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/>.= 
<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="c5">P</font>,<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="c5">P</font>,<font color="Maroon" title="c1">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="c4">k</font></span>)</span>,<font color="Maroon" title="c2">I</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1

;<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>
