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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: SCM_HALT:44</font></span><br/></a><div class="add"> 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">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="b3">I</font>, <font color="Olive" title="b4">J</font> being   <a href="amistd_1.html#V5" title="AMISTD_1:attr.5">really-closed</a>   <a href="scm_halt.html#V1" title="SCM_HALT:attr.1">InitHalting</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> <br/>  for <font color="Olive" title="b5">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> holds <br/> (  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">J</font>)</span>)</span>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">s</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="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b4">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3 &amp; ( <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">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 ( (  for <font color="Olive" title="b6">d</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">J</font>)</span>)</span>,<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="b6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<font color="Olive" title="b3">I</font>,<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="b6">d</font> ) &amp; (  for <font color="Olive" title="b6">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="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">J</font>)</span>)</span>,<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="b6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<font color="Olive" title="b3">I</font>,<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="b6">f</font> ) ) ) &amp; ( <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies ( (  for <font color="Olive" title="b6">d</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a> holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">J</font>)</span>)</span>,<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="b6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<font color="Olive" title="b4">J</font>,<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="b6">d</font> ) &amp; (  for <font color="Olive" title="b6">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="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b4">J</font>)</span>)</span>,<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="b6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K1" title="SCMFSA6B:func.1">IExec</a> (<font color="Olive" title="b4">J</font>,<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="b6">f</font> ) ) ) )</div></div>
