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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: SCMFSA_7:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">s</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Olive" title="b2">s</font> <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 holds <br/> for <font color="Olive" title="b3">a</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a><br/>  for <font color="Olive" title="b4">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b3">a</font> <a href="scmfsa_7.html#K1" title="SCMFSA_7:func.1">:=</a> <font color="Olive" title="b4">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> holds <br/>( <font color="Olive" title="b1">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Olive" title="b2">s</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">k</font> &amp; (  for <font color="Olive" title="b5">b</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a>  st <font color="Olive" title="b5">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">a</font> holds <br/><span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">b</font> ) &amp; (  for <font color="Olive" title="b5">f</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">f</font> ) )</div></div>
