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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th7</font></span>: <a NAME="T26"><span class="comment"><font color="firebrick">:: SCMFSA_9:26</font></span><br/></a><div class="add"> 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><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><br/>  for <font color="Olive" title="b4">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="b5">k</font>, <font color="Olive" title="b6">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">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="Olive" title="b1">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#K3" title="SCMFSA_X:func.3">while=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b4">s</font></span>)</span>,<font color="Olive" title="b6">n</font>) holds <br/>( <span class="p1">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">k</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">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="b5">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">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#K3" title="SCMFSA_X:func.3">while=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Olive" title="b4">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b1">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa_x.html#K3" title="SCMFSA_X:func.3">while=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>)</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">I</font></span>)</span>,<span class="p4">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K1" title="SCMFSA_9:func.1">StepWhile=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">P</font>,<font color="Olive" title="b4">s</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b5">k</font></span>)</span></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>) )</div></div>
