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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">c<sub>5</sub></font> be   <a href="scmpds_4.html#NM1">Program-block</a>;<br/>





<b>set </b><font color="Maroon">c<sub>6</sub></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">c<sub>5</sub></font></span>)</span>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:27"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E21</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">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:27"/><i><font color="Green">E22</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">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E4:27"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/>

<a NAME="E5:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green">E21</font></i></a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/>
<a NAME="E6:27"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E26</font></i>: 
 <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> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><a NAME="E2:27_1"/>
 <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> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E3:27_1"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E6:27"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmpds_7.html#E1:27_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/></div><b>end;</b></div>
<i><font color="Green">E26</font></i>:  <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> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
 <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> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self">Th26</a></i>
<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_7.html#E6:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>
;<br/>
<a NAME="E9:27"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></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">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/>
<a NAME="E10:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scmpds_6.html#T4">SCMPDS_6:4</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmpds_6.html#T37">SCMPDS_6:37</a></i>;<br/>
<a NAME="E12:27"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E9:27"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmpds_6.html#D3">SCMPDS_6:def 3</a></i>;<br/>
<b>hence </b><a NAME="E13:27"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E7:27"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_7.html#E8:27"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>

<a NAME="E14:27"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E12:27"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>;<br/>
<a NAME="E15:27"/>
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E6:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>;<br/>
<b>hence </b><a NAME="E16:27"/>
 <a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>3</sub></font>, <a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmpds_7.html#E2:27"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmpds_7.html#E3:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmpds_7.html#E4:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmpds_7.html#E14:27"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_7.html#T26" target="_self">Th26</a></i>;<br/>


</div>
