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<b>set </b><font color="Maroon">IF</font> =  <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font>;<br/>
<b>set </b><font color="Maroon">IsIF</font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">i</font> = <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">G</font> =  <a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">IJ</font> = <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font> as  <a href="scmpds_4.html#V3">shiftable</a> <a href="scmpds_4.html#NM1">Program-block</a> <b>by </b><i/>;<br/>
 <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4">';'</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" target="_self">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">J</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">J</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#T50">SCMPDS_4:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4">';'</a> <font color="Maroon">IJ</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#T50">SCMPDS_4:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">IJ</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#D4">SCMPDS_4:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E3:127_1_1"/>
 <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> is <a href="scmpds_4.html#V3">shiftable</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="127_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:127_1_1_2"/>
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/><a NAME="E2:127_1_1_2"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/><a NAME="E3:127_1_1_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">I</font> <a href="scmpds_6.html#R1" target="_self">is_closed_on</a> <font color="Maroon">s</font> &amp; <font color="Maroon">I</font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">s</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E4:127_1_1_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">J</font> <a href="scmpds_6.html#R1" target="_self">is_closed_on</a> <font color="Maroon">s</font> &amp; <font color="Maroon">J</font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">s</font> )
 <b>by </b><i>, </i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="127_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:127_1_1_2_1"/>
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="127_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:127_1_1_2_1_1"/>
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:127_1_1_2_1_1"/><b>then </b>
 <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34" target="_self">Th34</a>, <a class="ref" href="scmpds_6.html#T32" target="_self">Th32</a></i>;<br/><b>hence </b><a NAME="E3:127_1_1_2_1_1"/>
<font color="Maroon">s</font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="scmpds_6.html#D3" target="_self">Def3</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="127_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:127_1_1_2_1_2"/>
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:127_1_1_2_1_2"/><b>then </b>
 <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> <a href="scmpds_6.html#R2" target="_self">is_halting_on</a> <font color="Maroon">s</font>
 <b>by </b><i>, <a class="txt" href="scmpds_6.html#E34"><i><font color="Green">Lemma92</font></i></a></i>;<br/><b>hence </b><a NAME="E3:127_1_1_2_1_2"/>
<font color="Maroon">s</font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="scmpds_6.html#D3" target="_self">Def3</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E5:127_1_1"/><b>then </b>
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font></span>)</span></span>)</span> is <a href="ami_1.html#V12">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<b>hence </b><a NAME="E6:127_1_1"/>
 <a href="scmpds_6.html#K4" target="_self">if&lt;0</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font>,<font color="Maroon">I</font>,<font color="Maroon">J</font> is <a href="scmpds_4.html#V2">parahalting</a>
 <b>by </b><i><a class="ref" href="scmpds_4.html#D10">SCMPDS_4:def 10</a></i>;<br/>


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