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<b>let </b><font color="Maroon" title="c3">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">I</font> being <a href="scmpds_5.html#V3" title="SCMPDS_5:attr.3">No-StopCode</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b3">j</font> being <a href="scmpds_4.html#V4" title="SCMPDS_4:attr.4">shiftable</a> <a href="scmpds_5.html#V2" title="SCMPDS_5:attr.2">parahalting</a> <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Olive" title="b2">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b1">s</font> &amp; <font color="Olive" title="b2">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b1">s</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Olive" title="b3">j</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b3">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font></span><br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being <a href="scmpds_5.html#V3" title="SCMPDS_5:attr.3">No-StopCode</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">j</font> being <a href="scmpds_4.html#V4" title="SCMPDS_4:attr.4">shiftable</a> <a href="scmpds_5.html#V2" title="SCMPDS_5:attr.2">parahalting</a> <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Olive" title="b1">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Olive" title="b1">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Olive" title="b2">j</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font></span><br/><b>let </b><font color="Maroon" title="c5">I</font> be  <a href="scmpds_5.html#V3" title="SCMPDS_5:attr.3">No-StopCode</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">j</font> being <a href="scmpds_4.html#V4" title="SCMPDS_4:attr.4">shiftable</a> <a href="scmpds_5.html#V2" title="SCMPDS_5:attr.2">parahalting</a> <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Olive" title="b1">j</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font></span><br/><b>let </b><font color="Maroon" title="c6">j</font> be  <a href="scmpds_4.html#V4" title="SCMPDS_4:attr.4">shiftable</a> <a href="scmpds_5.html#V2" title="SCMPDS_5:attr.2">parahalting</a> <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font> implies <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c6">j</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> )</span><br/>







<b>assume </b><a NAME="E1:46"/><i><font color="Green" title="E38">A1</font></i>: 
( <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c6">j</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font></span><br/>

<b>set </b><font color="Maroon" title="c7">Mj</font> =  <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c6">j</font>;<br/>
<a NAME="E2:46"/>
for <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  holds  <span class="p1">(<span class="default"><a href="scmpds_5.html#K1" title="SCMPDS_5:func.1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font>
 
<b>by </b><i><a class="ref" href="scmpds_5.html#T40" title="SCMPDS_5:th.40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E3:46"/><b>then </b><i><font color="Green" title="E39">A2</font></i>: 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="scmpds_5.html#K1" title="SCMPDS_5:func.1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T23" title="SCMPDS_4:th.23">SCMPDS_4:23</a></i>;<br/>
<a NAME="E4:46"/><i><font color="Green" title="E40">A3</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="scmpds_2.html#D2" title="SCMPDS_2:def.2">SCMPDS_2:def 2</a></i>;<br/>
<a NAME="E5:46"/><i><font color="Green" title="E41">A4</font></i>: 
 <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c6">j</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T34" title="SCMPDS_6:th.34">SCMPDS_6:34</a></i>;<br/>
<a NAME="E6:46"/>
 <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c6">j</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T35" title="SCMPDS_6:th.35">SCMPDS_6:35</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c6">j</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c6">j</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:46"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="scmpds_7.html#E5:46"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="scmpds_7.html#T49" target="_self" title="SCMPDS_7:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1" title="SCMPDS_5:func.1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45" title="SCMPDS_5:th.45">SCMPDS_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1" title="SCMPDS_5:func.1">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E4:46"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a>, <a class="ref" href="scmpds_2.html#T100" title="SCMPDS_2:th.100">SCMPDS_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:46"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="scmpds_5.html#T44" title="SCMPDS_5:th.44">SCMPDS_5:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c6">j</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E4:46"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a>, <a class="ref" href="scmpds_2.html#T100" title="SCMPDS_2:th.100">SCMPDS_2:100</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
