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<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="scmfsa7b.html#V1">good</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>







<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green">E20</font></i>: 
(  <a href="sfmastr2.html#R1" target="_self">ProperTimesBody</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>6</sub></font> is <a href="scmfsa6b.html#V2">parahalting</a> )
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 or  not <font color="Maroon">c<sub>5</sub></font> is <a href="sf_mastr.html#V1">read-only</a> )
 ;<br/>

<a NAME="E4:26"/><i><font color="Green">E23</font></i>: 
 <a href="sfmastr2.html#R1" target="_self">ProperTimesBody</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E1:26"><i><font color="Green">E20</font></i></a>, <a class="ref" href="sfmastr2.html#T15" target="_self">Th15</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = 1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>
<a NAME="E5:26"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:26"><i><font color="Green">E21</font></i></a>, <a class="txt" href="sfmastr2.html#E4:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="sfmastr2.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E6:26"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:26"><i><font color="Green">E21</font></i></a>, <a class="txt" href="sfmastr2.html#E4:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="sfmastr2.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E7:26"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E5:26"><i><font color="Green">E24</font></i></a>, <a class="ref" href="sfmastr2.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E8:26"/>
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a> <span class="p1">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:26"><i><font color="Green">E21</font></i></a>, <a class="txt" href="sfmastr2.html#E4:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="sfmastr2.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E9:26"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E5:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="sfmastr2.html#E6:26"><i><font color="Green">E25</font></i></a>, <a class="ref" href="sfmastr2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E10:26"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:26"><i><font color="Green">E21</font></i></a>, <a class="txt" href="sfmastr2.html#E3:26"><i><font color="Green">E22</font></i></a>, <a class="txt" href="sfmastr2.html#E4:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="sfmastr2.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E11:26"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" target="_self">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="sfmastr1.html#K1">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font>
 
;<br/>
<a NAME="E12:26"/>
<font color="Maroon">c<sub>7</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:26"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>hence </b><a NAME="E13:26"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sfmastr2.html#K2" target="_self">StepTimes</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="sfmastr2.html#E5:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="sfmastr2.html#E7:26"><i><font color="Green">E26</font></i></a>, <a class="txt" href="sfmastr2.html#E9:26"><i><font color="Green">E27</font></i></a>, <a class="txt" href="sfmastr2.html#E11:26"><i><font color="Green">E28</font></i></a>, <a class="ref" href="sfmastr2.html#T20" target="_self">Th20</a></i>;<br/>


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