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<span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b3">J</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b4">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st (  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Olive" title="b1">p</font> or <font color="Olive" title="b3">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  ) &amp; <font color="Olive" title="b4">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">a</font> &amp; ( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Olive" title="b2">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">J</font>,<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b3">J</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">J</font>,<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b4">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b2">J</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st (  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font> or <font color="Olive" title="b2">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  ) &amp; <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> &amp; ( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Olive" title="b1">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b2">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b2">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b2">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">J</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st (  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font> or <font color="Olive" title="b1">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  ) &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> &amp; ( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c4">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b1">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">J</font> be   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st (  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font> or <font color="Maroon" title="c5">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  ) &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> &amp; ( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c4">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font> or <font color="Maroon" title="c5">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  ) &amp; <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> &amp; ( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c4">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  ) implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c7">UFLI</font> =  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c5">J</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
(  <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font> or <font color="Maroon" title="c5">J</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  )
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">and </span><br/><a NAME="E3:27"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
( <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c4">a</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">ST</font> =  <a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>);<br/>
<a NAME="E4:27"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="sfmastr2.html#T15" target="_self" title="SFMASTR2:th.15">Th15</a>, <a class="ref" href="sfmastr2.html#T16" target="_self" title="SFMASTR2:th.16">Th16</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">au</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">{</a><span class="default"><font color="Maroon" title="c4">a</font></span><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span>;<br/>
<a NAME="E5:27"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 <a href="sfmastr2.html#R1" title="SFMASTR2:pred.1">ProperTimesBody</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="sfmastr2.html#T15" target="_self" title="SFMASTR2:th.15">Th15</a></span>;<br/>
<a NAME="E6:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">{</a><span class="default"><font color="Maroon" title="c4">a</font></span><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="sfmastr2.html#T17" target="_self" title="SFMASTR2:th.17">Th17</a></span>;<br/>
<a NAME="E7:27"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="sfmastr2.html#D4" target="_self" title="SFMASTR2:def.4">Def4</a></span>;<br/>
<a NAME="E8:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span>,<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="sfmastr2.html#T4" target="_self" title="SFMASTR2:th.4">Th4</a></span>;<br/>
<a NAME="E9:27"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E10:27"/>
<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="sfmastr2.html#D4" target="_self" title="SFMASTR2:def.4">Def4</a></span>;<br/>
<a NAME="E11:27"/><span class="kw">then </span>
<font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span>,<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="sfmastr2.html#T5" target="_self" title="SFMASTR2:th.5">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="sfmastr2.html#K1" title="SFMASTR2:func.1">times*</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K3" title="SFMASTR2:func.3">StepTimes</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">s</font>)</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c6">k</font></span>)</span>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="sfmastr2.html#T20" target="_self" title="SFMASTR2:th.20">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>

<span class="kw">set </span><font color="Maroon" title="c11">UILI</font> =  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">J</font>;<br/>

</div>
