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<span class="kw">set </span><font color="Maroon" title="c2">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="c3">II</font> =  <a href="compos_1.html#K14" title="COMPOS_1:func.14">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">II</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  &amp; <font color="Maroon" title="c3">II</font> is  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  &amp; <font color="Maroon" title="c3">II</font> is  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">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="c3">II</font> implies <font color="Maroon" title="c3">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> )</span><br/><span class="kw">assume </span><a NAME="E1:37_1_1_1"/>
<font color="Maroon" title="c4">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="c3">II</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span><br/><a NAME="E2:37_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">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#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><a NAME="E3:37_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">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="E4:37_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c3">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>;<br/><a NAME="E5:37_1_1_1"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">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#T14" title="SCMPDS_2:th.14">SCMPDS_2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:37_1_1_1"/>
<font color="Maroon" title="c3">II</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="#E4:37_1_1_1"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="scmpds_2.html#T12" title="SCMPDS_2:th.12">SCMPDS_2:12</a>, <a class="ref" href="scmpds_2.html#T81" title="SCMPDS_2:th.81">SCMPDS_2:81</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:37_1_1"/>
( <font color="Maroon" title="c3">II</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  &amp; <font color="Maroon" title="c3">II</font> is  <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>  &amp; <font color="Maroon" title="c3">II</font> is  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D25" title="COMPOS_1:def.25">COMPOS_1:def 25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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