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<b>let </b><font color="Maroon">c<sub>2</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>3</sub></font> be  <a href="scm_halt.html#V2" target="_self">InitHalting</a> <a href="scm_halt.html#V3" target="_self">keepInt0_1</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>



<a NAME="E1:25"/><i><font color="Green">E18</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E2:25"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="scm_halt.html#T5" target="_self">Th5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:25"/><i><font color="Green">E19</font></i>: 
(  <a href="ami_1.html#K12">Result</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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>  )
 <b>by </b><i><a class="ref" href="ami_1.html#D22">AMI_1:def 22</a></i>;<br/>
<a NAME="E5:25"/>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_1"/><i><font color="Green">E20</font></i>: 
 <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/>

<a NAME="E2:25_1"/>
 <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/>
<b>hence </b><a NAME="E3:25_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:25_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmfsa_2.html#T13">SCMFSA_2:13</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:25"/><b>then </b><i><font color="Green">E20</font></i>: 
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1">SCMFSA6B:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E6:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="scm_halt.html#E1:25"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scm_halt.html#E4:25"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scm_halt.html#D3" target="_self">Def3</a></i>
;<br/>


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