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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="scmpds_4.html#NM1">Program-block</a>;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:3"/><i><font color="Green">E5</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="scmpds_3.html#K5">SCMPDS-Stop</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="scmpds_3.html#K6">Shift</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> ,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E3:3"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6">Shift</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> ,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:3"><i><font color="Green">E4</font></i></a>, <a class="txt" href="scmpds_5.html#E2:3"><i><font color="Green">E5</font></i></a>, <a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/>
<a NAME="E4:3"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_3.html#K3">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> where B is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmpds_3.html#T38">SCMPDS_3:38</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <b> such that </b><br/><a NAME="E6:3"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmpds_3.html#K3">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a>  )
 ;<br/>
<a NAME="E7:3"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 0
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:3"><i><font color="Green">E6</font></i></a>, <a class="ref" href="scmpds_4.html#T72">SCMPDS_4:72</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>

<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:3"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scmpds_5.html#E7:3"><i><font color="Green">E7</font></i></a>, <a class="ref" href="scmpds_4.html#T38">SCMPDS_4:38</a>, <a class="ref" href="scmpds_4.html#T73">SCMPDS_4:73</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">E4</font></i></a></i>;<br/>


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