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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th48</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: SCMFSA9A:48</font></span><br/></a><div class="add"> 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">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="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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><br/>  for <font color="Olive" title="b5">J</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">really-closed</a>  <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>   st  not <font color="Olive" title="b5">J</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b4">a</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="Olive" title="b3">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_halting_on</a> <span class="p1">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="Olive" title="b3">k</font>,<font color="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">Times</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>)</span>)</span> holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="p2">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="Olive" title="b3">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="p2">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa9a.html#K4" title="SCMFSA9A:func.4">StepTimes</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">J</font>,<font color="Olive" title="b2">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="Olive" title="b3">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 ) )</div></div>
