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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="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">c<sub>5</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>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</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>3</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></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> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</sub></font>;<br/>
<b>assume </b><a NAME="E1:46"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:46"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>5</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>3</sub></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/>
<b>assume </b><a NAME="E3:46"/>
 <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">c<sub>5</sub></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> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</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="E4:46"/><b>then </b>
 <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">c<sub>5</sub></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">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</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> 
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:46"><i><font color="Green">E35</font></i></a>, <a class="ref" href="scmpds_6.html#T41">SCMPDS_6:41</a></i>;<br/>
<b>hence </b><a NAME="E5:46"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_7.html#E1:46"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmpds_7.html#E2:46"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>


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