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<div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="scm_halt.html#V2" target="_self">InitHalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>



<b>assume </b><a NAME="E1:88"/><i><font color="Green">E63</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:88"/><b>then </b><i><font color="Green">E64</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="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="ami_1.html#K6">IC</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>4</sub></font></span>)</span></span>)</span>;<br/>
<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:88_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="ami_1.html#K6">IC</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>9</sub></font></span>)</span>;<br/><a NAME="E2:88_1"/><i><font color="Green">E66</font></i>: 
<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> <font color="Maroon">c<sub>9</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:88"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scm_halt.html#E2:88"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scm_halt.html#E1:88_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scm_halt.html#T65" target="_self">Th65</a></i>;<br/><a NAME="E3:88_1"/><i><font color="Green">E67</font></i>: 
 <a href="ami_1.html#K6">IC</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>9</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:88"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scm_halt.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E4:88_1"/><i><font color="Green">E68</font></i>: 
 <a href="ami_1.html#K6">IC</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>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:88_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmfsa6a.html#T29">SCMFSA6A:29</a></i>;<br/><a NAME="E5:88_1"/><i><font color="Green">E69</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T106">SCMFSA8C:106</a></i>;<br/><b>assume </b><a NAME="E6:88_1"/><i><font color="Green">E70</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><i><font color="Green">E71</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> = 
<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>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>9</sub></font></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"><span class="p3">(<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>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E4:88_1"><i><font color="Green">E68</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></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"><span class="p3">(<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>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<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>9</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E3:88_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scm_halt.html#E5:88_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/><a NAME="E8:88_1"/>
<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<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>9</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_halt.html#E3:88_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scm_halt.html#E5:88_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E9:88_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scm_halt.html#E6:88_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scm_halt.html#E7:88_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmfsa8c.html#T107">SCMFSA8C:107</a></i>;<br/></div>
<b>end;</b></div>


</div>
