<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">I</font> be  <a href="scmpds_5.html#V3">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/>



<b>set </b><font color="Maroon">II</font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">si</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:35"/><i><font color="Green">E49</font></i>: 
(  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> &amp; <font color="Maroon">I</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">s</font> &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">I</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:35"/><i><font color="Green">E50</font></i>: 
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<a NAME="E3:35"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/>
<a NAME="E4:35"/><i><font color="Green">E54</font></i>: 
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E5:35"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i>, <a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/>
<a NAME="E6:35"/><i><font color="Green">E56</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 
<b>by </b><i>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<a NAME="E7:35"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T17">SCMPDS_6:17</a></i>;<br/>
<a NAME="E8:35"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  = 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i>, , , <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>
<br/>.= 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_6.html#T21">SCMPDS_6:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i>, , , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">I</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
<b>by </b><i>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>
<b>hence </b><a NAME="E10:35"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmpds_5.html#D3">SCMPDS_5:def 3</a></i>;<br/>


</div>
