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<span class="kw">let </span><font color="Maroon" title="c4">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">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="b2">I</font>, <font color="Olive" title="b3">J</font> being   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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">a</font>, <font color="Olive" title="b5">b</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Olive" title="b2">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b4">a</font> &amp;  not <font color="Olive" title="b3">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b4">a</font> holds <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">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#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b3">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 &amp; ( <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">b</font> implies ( (  for <font color="Olive" title="b6">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</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#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b6">d</font> ) &amp; (  for <font color="Olive" title="b6">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b6">f</font> ) ) ) &amp; ( <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">b</font> implies ( (  for <font color="Olive" title="b6">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</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#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b3">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b6">d</font> ) &amp; (  for <font color="Olive" title="b6">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</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#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b3">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b6">f</font> ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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">I</font>, <font color="Olive" title="b2">J</font> being   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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">a</font>, <font color="Olive" title="b4">b</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b3">a</font> &amp;  not <font color="Olive" title="b2">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b3">a</font> holds <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">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#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b4">b</font> implies ( (  for <font color="Olive" title="b5">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">d</font> <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">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">d</font> ) &amp; (  for <font color="Olive" title="b5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b5">f</font> <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">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b5">f</font> ) ) ) &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b4">b</font> implies ( (  for <font color="Olive" title="b5">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">d</font> <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>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b5">d</font> ) &amp; (  for <font color="Olive" title="b5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b5">f</font> <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>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b5">f</font> ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">I</font>, <font color="Maroon" title="c7">J</font> be   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b1">a</font> &amp;  not <font color="Maroon" title="c7">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Olive" title="b1">a</font> holds <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">b</font> implies ( (  for <font color="Olive" title="b3">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">d</font> ) &amp; (  for <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> ) ) ) &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">b</font> implies ( (  for <font color="Olive" title="b3">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">d</font> ) &amp; (  for <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> ) ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <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"> (  not <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Maroon" title="c8">a</font> &amp;  not <font color="Maroon" title="c7">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Maroon" title="c8">a</font> implies (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
 not <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Maroon" title="c8">a</font>
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
 not <font color="Maroon" title="c7">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">refers</a> <font color="Maroon" title="c8">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">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#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">JJ</font> =  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) as   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">II</font> =  <a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span> as   <a href="scmfsa6b.html#V1" title="SCMFSA6B:attr.1">keeping_0</a>   <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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/>
<span class="kw">set </span><font color="Maroon" title="c12">i</font> =  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c13">s1</font> =  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>);<br/>
<div><span class="lab"><font color="Green" title="E37">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">c</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <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"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font> implies <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font> )</span><br/><span class="kw">assume </span><a NAME="E1:45_1"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 ; <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"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E6:45"/>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p1">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">IncIC</a> (<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c11">II</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">II</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T20" title="SCMFSA6B:th.20">SCMFSA6B:20</a></span>;<br/>
<span class="kw">hence </span> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p3">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c11">II</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">II</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T113" title="FUNCT_4:th.113">FUNCT_4:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">II</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T18" target="_self" title="SCMFSA8B:th.18">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T56" title="COMPOS_1:th.56">COMPOS_1:56</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5

;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) &amp; ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) ) )</span><br/>

<div><span class="lab"><font color="Green" title="E38">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</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"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></span>
<br/>.= 
<font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</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/></div><span class="kw">end;</span></div>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font> implies ( (  for <font color="Olive" title="b1">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) ) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:45_4"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font>
 ; <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">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) )</span><br/><a NAME="E2:45_4"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c6">I</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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T18" title="SCMFSA7B:th.18">SCMFSA7B:18</a></span>;<br/><a NAME="E3:45_4"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<font color="Maroon" title="c6">I</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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T19" title="SCMFSA7B:th.19">SCMFSA7B:19</a></span>;<br/><span class="lab"><font color="Green" title="E42">A8</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_4"><span class="lab"><font color="Green" title="E39">A5</font></span></a></span>
;<br/><div><span class="kw">hereby </span> <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">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font></span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c14">d</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"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d</font> implies <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> )</span><br/><span class="kw">assume </span><a NAME="E1:45_4_2"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d</font>
 ; <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"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T9" target="_self" title="SCMFSA8B:th.9">Th12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_4"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="ref" href="scmfsa8b.html#T18" target="_self" title="SCMFSA8B:th.18">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E8:45"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E2:45_4"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E3:45_4"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E1:45_4_2"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="scmfsa8b.html#T38" target="_self" title="SCMFSA8B:th.38">Th41</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/></div>
<span class="kw">end;</span></div><span class="kw">let </span><font color="Maroon" title="c14">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</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"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> <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="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T10" target="_self" title="SCMFSA8B:th.10">Th13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45_4"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="ref" href="scmfsa8b.html#T18" target="_self" title="SCMFSA8B:th.18">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E8:45"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E2:45_4"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E3:45_4"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="scmfsa8b.html#T38" target="_self" title="SCMFSA8B:th.38">Th41</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/></div>
<span class="kw">end;</span></div>

<span class="lab"><font color="Green" title="E39">A10</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T65" title="SCMFSA_2:th.65">SCMFSA_2:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>
;<br/>
<a NAME="E11:45"/><span class="lab"><font color="Green" title="E40">A11</font></span>: 
<font color="Maroon" title="c7">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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T19" title="SCMFSA7B:th.19">SCMFSA7B:19</a></span>;<br/>
<a NAME="E12:45"/><span class="lab"><font color="Green" title="E41">A12</font></span>: 
<font color="Maroon" title="c7">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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T18" title="SCMFSA7B:th.18">SCMFSA7B:18</a></span>;<br/>
<span class="kw">assume </span><a NAME="E13:45"/>
<font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font>
 ; <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">d</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">d</font> ) &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> ) )</span><br/>

<a NAME="E14:45"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A13</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span>
 
;<br/>
<div><span class="kw">hereby </span> <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">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font></span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c14">d</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"> ( <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d</font> implies <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> )</span><br/><span class="kw">assume </span><a NAME="E1:45_6"/><span class="lab"><font color="Green" title="E43">A14</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d</font>
 ; <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"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T9" target="_self" title="SCMFSA8B:th.9">Th12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:45"><span class="lab"><font color="Green" title="E39">A10</font></span></a>, <a class="txt" href="#E14:45"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="ref" href="scmfsa8b.html#T18" target="_self" title="SCMFSA8B:th.18">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c14">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E8:45"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E12:45"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="txt" href="#E11:45"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="txt" href="#E1:45_6"><span class="lab"><font color="Green" title="E43">A14</font></span></a>, <a class="ref" href="scmfsa8b.html#T38" target="_self" title="SCMFSA8B:th.38">Th41</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/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c14">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</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"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> <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="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c10">JJ</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T10" target="_self" title="SCMFSA8B:th.10">Th13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c4">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:45"><span class="lab"><font color="Green" title="E39">A10</font></span></a>, <a class="txt" href="#E14:45"><span class="lab"><font color="Green" title="E42">A13</font></span></a>, <a class="ref" href="scmfsa8b.html#T18" target="_self" title="SCMFSA8B:th.18">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c5">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E8:45"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E12:45"><span class="lab"><font color="Green" title="E41">A12</font></span></a>, <a class="txt" href="#E11:45"><span class="lab"><font color="Green" title="E40">A11</font></span></a>, <a class="ref" href="scmfsa8b.html#T38" target="_self" title="SCMFSA8B:th.38">Th41</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/>


</div>
