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<span class="kw">set </span><font color="Maroon" title="c1">ii</font> = <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">take </span><font color="Maroon" title="c2">II</font> =  <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">II</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  &amp; <font color="Maroon" title="c2">II</font> is  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  &amp; <font color="Maroon" title="c2">II</font> is  <a href="ami_1.html#V6" title="AMI_1:attr.6">halt-free</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">II</font> implies <font color="Maroon" title="c2">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:41_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">II</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span><br/><a NAME="E2:41_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/><a NAME="E3:41_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:41_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c2">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/><a NAME="E5:41_1_1_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T23" title="SCMPDS_2:th.23">SCMPDS_2:23</a></span>;<br/><span class="kw">hence </span><a NAME="E6:41_1_1_1"/>
<font color="Maroon" title="c2">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_1_1_1"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="scmpds_2.html#T21" title="SCMPDS_2:th.21">SCMPDS_2:21</a>, <a class="ref" href="scmpds_2.html#T93" title="SCMPDS_2:th.93">SCMPDS_2:93</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:41_1_1"/>
( <font color="Maroon" title="c2">II</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  &amp; <font color="Maroon" title="c2">II</font> is  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  &amp; <font color="Maroon" title="c2">II</font> is  <a href="ami_1.html#V6" title="AMI_1:attr.6">halt-free</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#D3" target="_self" title="SCMPDS_5:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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