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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="scm_halt.html#V2" target="_self">InitHalting</a>
 <b>and </b><br/><a NAME="E2:16_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="scm_halt.html#V2" target="_self">InitHalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a> <b>by </b><i><a class="txt" href="scm_halt.html#E1:16_1_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>  <a href="subset_1.html#M2">M3</a>(<a href="zfmisc_1.html#K2">K19</a>(the <a href="ami_1.html#U3">Instruction-Codes</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">K3</a>(<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="numbers.html#K4">INT</a> ,<a href="finseq_2.html#K3">K225</a>(<a href="numbers.html#K4">INT</a> )</span><a href="tarski.html#K2">}</a></span>) <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span>),the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ) =  <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>  <a href="subset_1.html#M2">M3</a>( <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K5">NAT</a> ) = 1;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  =  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K4">INT</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E5:16_1_1"/><i><font color="Green">E13</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 <b>and </b><br/><a NAME="E6:16_1_1"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) &amp; <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) &amp; <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) )
 <b>from </b><i><a class="ref" href="scmfsa6a.html#S1">SCMFSA6A:sch 1</a>();<br/></i>
<a NAME="E7:16_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E2:16_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E8:16_1_1"/><i><font color="Green">E16</font></i>: 
 <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T66">SCMFSA_2:66</a></i>;<br/>
<a NAME="E9:16_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="scm_halt.html#E6:16_1_1"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E10:16_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="scmfsa_3.html#K1">.--&gt;</a> 1 <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E8:16_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="scmfsa6a.html#T7">SCMFSA6A:7</a></i>;<br/>
<a NAME="E11:16_1_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="scmfsa_3.html#K1">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E7:16_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmfsa6a.html#T6">SCMFSA6A:6</a></i>;<br/>
<a NAME="E12:16_1_1"/><i><font color="Green">E18</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T25">AMI_5:25</a></i>;<br/>
<a NAME="E13:16_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 
<b>by </b><i><a class="txt" href="scm_halt.html#E5:16_1_1"><i><font color="Green">E13</font></i></a></i>;<br/>
<a NAME="E14:16_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E12:16_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="scmfsa6a.html#T7">SCMFSA6A:7</a></i>;<br/>
<a NAME="E15:16_1_1"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="ami_3.html#D12">AMI_3:def 12</a></i>;<br/>
<a NAME="E16:16_1_1"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="scmfsa_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#D3">SCMFSA6A:def 3</a></i>;<br/>
<a NAME="E17:16_1_1"/><b>then </b>
 <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>4</sub></font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E11:16_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scm_halt.html#E15:16_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmfsa6a.html#T6">SCMFSA6A:6</a></i>;<br/>
<a NAME="E18:16_1_1"/><b>then </b><i><font color="Green">E20</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/>
<a NAME="E19:16_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E6:16_1_1"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E20:16_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scm_halt.html#E5:16_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scm_halt.html#E18:16_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmfsa6b.html#T24">SCMFSA6B:24</a></i>;<br/>


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