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<div class="add">

<b>set </b><font color="Maroon" title="c7">IF</font> =  <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font>;<br/>
<b>set </b><font color="Maroon" title="c8">IsIF</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">i</font> = <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</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="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">G</font> =  <a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</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="c4">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">IJ</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font> as  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a> <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a> <b>by </b><i><a class="txt" href="scmpds_6.html#E51"><i><font color="Green" title="E43">Lm3</font></i></a></i>;<br/>
 <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K1" title="SCMPDS_6:func.1">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c4">J</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#T50" title="SCMPDS_4:th.50">SCMPDS_4:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <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="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <font color="Maroon" title="c11">IJ</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#T50" title="SCMPDS_4:th.50">SCMPDS_4:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <font color="Maroon" title="c11">IJ</font>
<b>by </b><i><a class="ref" href="scmpds_4.html#D4" title="SCMPDS_4:def.4">SCMPDS_4:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E3:65_1_1"/>
 <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> is <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:65_1_1_2"/>
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s</font>
 ;<br/><a NAME="E2:65_1_1_2"/><b>then </b><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c12">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">s</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/><a NAME="E3:65_1_1_2"/><i><font color="Green" title="E56">A2</font></i>: 
( <font color="Maroon" title="c3">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">s</font> &amp; <font color="Maroon" title="c3">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">s</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34" target="_self" title="SCMPDS_6:th.34">Th34</a>, <a class="ref" href="scmpds_6.html#T35" target="_self" title="SCMPDS_6:th.35">Th35</a></i>;<br/><a NAME="E4:65_1_1_2"/><i><font color="Green" title="E57">A3</font></i>: 
( <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">s</font> &amp; <font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">s</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34" target="_self" title="SCMPDS_6:th.34">Th34</a>, <a class="ref" href="scmpds_6.html#T35" target="_self" title="SCMPDS_6:th.35">Th35</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_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="E1:65_1_1_2_1"/>
( <font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:65_1_1_2_1_1"/>
<font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:65_1_1_2_1_1"/><b>then </b>
 <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">s</font>
 <b>by </b><i><a class="txt" href="scmpds_6.html#E3:65_1_1_2"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="scmpds_6.html#T52" target="_self" title="SCMPDS_6:th.52">Th52</a></i>;<br/><b>hence </b><a NAME="E3:65_1_1_2_1_1"/>
<font color="Maroon" title="c12">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="txt" href="scmpds_6.html#E2:65_1_1_2"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="scmpds_6.html#D3" target="_self" title="SCMPDS_6:def.3">Def3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:65_1_1_2_1_2"/>
<font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>,<font color="Maroon" title="c6">k1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:65_1_1_2_1_2"/><b>then </b>
 <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">s</font>
 <b>by </b><i><a class="txt" href="scmpds_6.html#E4:65_1_1_2"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="scmpds_6.html#T53" target="_self" title="SCMPDS_6:th.53">Th53</a></i>;<br/><b>hence </b><a NAME="E3:65_1_1_2_1_2"/>
<font color="Maroon" title="c12">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="txt" href="scmpds_6.html#E2:65_1_1_2"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="scmpds_6.html#D3" target="_self" title="SCMPDS_6:def.3">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E5:65_1_1"/><b>then </b>
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font></span>)</span></span>)</span> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a></i>;<br/>
<b>hence </b><a NAME="E6:65_1_1"/>
 <a href="scmpds_6.html#K2" title="SCMPDS_6:func.2">if=0</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">k1</font>,<font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c4">J</font> is <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>
 <b>by </b><i><a class="ref" href="scmpds_4.html#D10" title="SCMPDS_4:def.10">SCMPDS_4:def 10</a></i>;<br/>


</div>
