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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: SCMRING4:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">R</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b2">R</font><br/>  for <font color="Olive" title="b5">s1</font>, <font color="Olive" title="b6">s2</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b2">R</font></span>)</span><br/>  for <font color="Olive" title="b7">P1</font>, <font color="Olive" title="b8">P2</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b2">R</font></span>)</span><br/>  for <font color="Olive" title="b9">q</font> being   <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b10">p</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>9</sub></font> <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b2">R</font></span>)</span>  st <font color="Olive" title="b10">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">s1</font> &amp; <font color="Olive" title="b10">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">s2</font> &amp; <font color="Olive" title="b9">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b7">P1</font> &amp; <font color="Olive" title="b9">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b8">P2</font> &amp;  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Olive" title="b7">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b7">P1</font>,<font color="Olive" title="b5">s1</font>,<font color="Olive" title="b1">n</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K4" title="SCMRING2:func.4">AddTo</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) &amp; <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b10">p</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b7">P1</font>,<font color="Olive" title="b5">s1</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b7">P1</font>,<font color="Olive" title="b5">s1</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b8">P2</font>,<font color="Olive" title="b6">s2</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b8">P2</font>,<font color="Olive" title="b6">s2</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="scmring2.html#K2" title="SCMRING2:func.2">.</a> <font color="Olive" title="b4">b</font></span>)</span></div></div>
