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<b>let </b><font color="Maroon">c<sub>2</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>3</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>4</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>5</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>







<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="scmfsa6b.html#V2">parahalting</a> or ( <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="scmfsa6b.html#V2">parahalting</a> or ( <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) )
 ;<br/>

<a NAME="E3:25"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E1:25"><i><font color="Green">E12</font></i></a>, <a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/>
<a NAME="E4:25"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E2:25"><i><font color="Green">E13</font></i></a>, <a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/>
<a NAME="E5:25"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="scmfsa6b.html#V2">parahalting</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="scmfsa6b.html#V1">paraclosed</a> )
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E10"><i><font color="Green">Lemma10</font></i></a></i>;<br/>
<a NAME="E6:25"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E1:25"><i><font color="Green">E12</font></i></a>, <a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a></i>;<br/>
<a NAME="E7:25"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="scmfsa6b.html#V2">parahalting</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="scmfsa6b.html#V1">paraclosed</a> )
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E10"><i><font color="Green">Lemma10</font></i></a></i>;<br/>
<a NAME="E8:25"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E2:25"><i><font color="Green">E13</font></i></a>, <a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a></i>;<br/>
<a NAME="E9:25"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sfmastr1.html#E3:25"><i><font color="Green">E14</font></i></a>, <a class="txt" href="sfmastr1.html#E4:25"><i><font color="Green">E15</font></i></a>, <a class="txt" href="sfmastr1.html#E6:25"><i><font color="Green">E16</font></i></a>, <a class="ref" href="sfmastr1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E10:25"/>
not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T9">SCMFSA6B:9</a></i>;<br/>
<b>hence </b><a NAME="E11:25"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sfmastr1.html#E9:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>


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