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<b>let </b><font color="Maroon" title="c1">loc</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c2">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E4">A1</font></i>: 
( <font color="Maroon" title="c1">loc</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">loc</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>  )
 ;<br/>

<b>assume </b><a NAME="E2:3"/><i><font color="Green" title="E5">A2</font></i>: 
not <font color="Maroon" title="c1">loc</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">I</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c3">SS</font> =  <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a> ;<br/>
<b>set </b><font color="Maroon" title="c4">S2</font> =  <a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a> ,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span>;<br/>
<a NAME="E3:3"/>
<font color="Maroon" title="c1">loc</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a> ,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="scmpds_5.html#E2:3"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></i>;<br/>
<a NAME="E4:3"/><b>then </b>
<font color="Maroon" title="c1">loc</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">l1</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : <font color="Olive" title="b1">l1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmpds_3.html#T38" title="SCMPDS_3:th.38">SCMPDS_3:38</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">l1</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E6:3"/><i><font color="Green" title="E6">A3</font></i>: 
( <font color="Maroon" title="c1">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> &amp; <font color="Maroon" title="c5">l1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a>  )
 ;<br/>
<a NAME="E7:3"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmpds_3.html#K5" title="SCMPDS_3:func.5">SCMPDS-Stop</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E8:3"/><b>then </b>
<font color="Maroon" title="c5">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:3"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_5.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="scmpds_5.html#E6:3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="scmpds_4.html#T38" title="SCMPDS_4:th.38">SCMPDS_4:38</a>, <a class="ref" href="scmpds_4.html#T73" title="SCMPDS_4:th.73">SCMPDS_4:73</a></i>;<br/>


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