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<span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/>  for <font color="Olive" title="b4">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b3">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b3">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c3">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/>  for <font color="Olive" title="b3">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/>  for <font color="Olive" title="b2">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">MacroInstruction</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="scmfsa_m.html#NV2" title="SCMFSA_M:NV.2">read-write</a>  <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span><br/>









<span class="kw">set </span><font color="Maroon" title="c7">sk</font> = <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">sk0</font> = <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>;<br/>
<a NAME="E1:48"/>
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D2" target="_self" onmouseover="rs('scmfsa_9/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">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="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa_x.html#K4" title="SCMFSA_X:func.4">while&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D2" target="_self" onmouseover="rs('scmfsa_9/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_9.html#D2" target="_self" onmouseover="rs('scmfsa_9/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">StepWhile&gt;0</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1

;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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