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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: SCM_COMP:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a><br/>  for <font color="Olive" title="b2">term</font> being   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/>  for <font color="Olive" title="b3">aux</font>, <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> (<font color="Olive" title="b2">term</font>,<font color="Olive" title="b3">aux</font>)</span>)</span>,<font color="Olive" title="b4">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> holds <br/> for <font color="Olive" title="b5">s</font> being  <font color="Olive">b<sub>4</sub></font> <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <font color="Olive" title="b3">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K17" title="SCM_COMP:func.17">max_Data-Loc_in</a> <font color="Olive" title="b2">term</font> holds <br/> ex <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b7">u</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> st <br/>( <font color="Olive" title="b7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b5">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) &amp; <font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> (<font color="Olive" title="b2">term</font>,<font color="Olive" title="b3">aux</font>)</span>)</span> &amp;  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b5">s</font>,<font color="Olive" title="b6">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b6">i</font> &amp;  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Olive" title="b7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b7">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Olive" title="b3">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">term</font> <a href="scm_comp.html#K12" title="SCM_COMP:func.12">@</a> <font color="Olive" title="b5">s</font> &amp; (  for <font color="Olive" title="b8">dn</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b8">dn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">aux</font> holds <br/><font color="Olive" title="b5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Olive" title="b8">dn</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Olive" title="b8">dn</font></span>)</span> ) )</div></div>
