<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">la</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/>



<b>reconsider </b><font color="Maroon" title="c3">a3</font> = <font color="Maroon" title="c1">la</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c4">mj</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> <b> such that </b><br/><a NAME="E3:99"/><i><font color="Green" title="E66">A1</font></i>: 
( <font color="Maroon" title="c4">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a3</font> &amp;  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c4">mj</font> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c5">L</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E5:99"/><i><font color="Green" title="E67">A2</font></i>: 
( <font color="Maroon" title="c5">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">mj</font> &amp;  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c4">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c5">L</font> )
 <b>by </b><i><a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">s</font> being   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>;<br/>
<b>set </b><font color="Maroon" title="c7">t</font> = <font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">f</font> = the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>
<a NAME="E7:99"/><i><font color="Green" title="E68">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E8:99"/><b>then </b>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E69">A4</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 = 
<span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<a NAME="E10:99"/><b>then </b><i><font color="Green" title="E70">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">L</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E3:99"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E5:99"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a>, <a class="ref" href="ami_2.html#D2" title="AMI_2:def.2">AMI_2:def 2</a>, <a class="ref" href="ami_2.html#D3" title="AMI_2:def.3">AMI_2:def 3</a></i>;<br/>
<a NAME="E11:99"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<a NAME="E12:99"/><b>then </b><i><font color="Green" title="E71">A6</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E13:99"/><i><font color="Green" title="E72">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<i><font color="Green" title="E73">A8</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E13:99"><i><font color="Green" title="E72">A7</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>
<br/>.= 
 <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E12:99"><i><font color="Green" title="E71">A6</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/>
<a NAME="E15:99"/><i><font color="Green" title="E74">A9</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E16:99"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:99_3"/><i><font color="Green" title="E75">A10</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:99_3_1"/>
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c9">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_3_1_1"><b>suppose </b></a><a NAME="E1:99_3_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:99_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E9:99"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="scmfsa_1.html#T9" title="SCMFSA_1:th.9">SCMFSA_1:9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_3_1_2"><b>suppose </b></a><a NAME="E1:99_3_1_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:99_3_1_2"/><b>then </b>
not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E7:99"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:99_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E4:99_3_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:99_3"><i><font color="Green" title="E75">A10</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c9">t</font> = <font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c3">a3</font></span>)</span></span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa_2.html#E14:99"><i><font color="Green" title="E73">A8</font></i></a>, <a class="txt" href="scmfsa_2.html#E15:99"><i><font color="Green" title="E74">A9</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">w</font> = <font color="Maroon" title="c9">t</font> as   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ;<br/>
<a NAME="E19:99"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E20:99"/><b>then </b>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E75">A11</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c10">w</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 = 
<span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c1">la</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<b>assume </b><a NAME="E22:99"/><i><font color="Green" title="E76">A12</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c1">la</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_5"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:99_5"/>
( <font color="Maroon" title="c9">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 or <font color="Maroon" title="c9">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_5_1"><b>suppose </b></a><a NAME="E1:99_5_1"/><i><font color="Green" title="E77">A13</font></i>: 
<font color="Maroon" title="c9">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:99_5_1"/><i><font color="Green" title="E78">A14</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">IC</a> <font color="Maroon" title="c10">w</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T102" target="_self" title="SCMFSA_2:th.102">Th102</a></i>;<br/><a NAME="E3:99_5_1"/><i><font color="Green" title="E79">A15</font></i>: 
 <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">IC</a> <font color="Maroon" title="c10">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D16" title="SCMFSA_1:def.16">SCMFSA_1:def 16</a></i>;<br/><a NAME="E4:99_5_1"/><i><font color="Green" title="E80">A16</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c1">la</font></span>)</span>,<font color="Maroon" title="c9">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E22:99"><i><font color="Green" title="E76">A12</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a>, <a class="txt" href="scmfsa_2.html#E2:99_5_1"><i><font color="Green" title="E78">A14</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:99_5_1"><i><font color="Green" title="E79">A15</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">e</font> = <font color="Maroon" title="c10">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 as   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:99_5_1"><i><font color="Green" title="E79">A15</font></i></a></i>;<br/><a NAME="E6:99_5_1"/><i><font color="Green" title="E81">A17</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c1">la</font></span>)</span>,<font color="Maroon" title="c9">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c11">e</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:99_5_1"><i><font color="Green" title="E77">A13</font></i></a>, <a class="txt" href="scmfsa_2.html#E2:99_5_1"><i><font color="Green" title="E78">A14</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:99_5_1"><i><font color="Green" title="E79">A15</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" target="_self" title="SCMFSA_2:th.96">Th96</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">mi</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> <b> such that </b><br/><a NAME="E8:99_5_1"/><i><font color="Green" title="E82">A18</font></i>: 
( <font color="Maroon" title="c12">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e</font> &amp;  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c11">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c12">mi</font> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D9" target="_self" title="SCMFSA_2:def.9">Def9</a></i>;<br/><b>consider </b><font color="Maroon" title="c13">L1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E10:99_5_1"/><i><font color="Green" title="E83">A19</font></i>: 
( <font color="Maroon" title="c13">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">mi</font> &amp;  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c12">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K17" title="AMI_2:func.17">Next</a> <font color="Maroon" title="c13">L1</font> )
 <b>by </b><i><a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>;<br/><a NAME="E11:99_5_1"/>
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c11">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">L1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E8:99_5_1"><i><font color="Green" title="E82">A18</font></i></a>, <a class="txt" href="scmfsa_2.html#E10:99_5_1"><i><font color="Green" title="E83">A19</font></i></a>, <a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a>, <a class="ref" href="ami_2.html#T2" title="AMI_2:th.2">AMI_2:2</a>, <a class="ref" href="ami_2.html#T3" title="AMI_2:th.3">AMI_2:3</a></i>;<br/><b>hence </b><a NAME="E12:99_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:99_5_1"><i><font color="Green" title="E80">A16</font></i></a>, <a class="txt" href="scmfsa_2.html#E6:99_5_1"><i><font color="Green" title="E81">A17</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:99_5_1"><i><font color="Green" title="E82">A18</font></i></a>, <a class="txt" href="scmfsa_2.html#E10:99_5_1"><i><font color="Green" title="E83">A19</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_5_2"><b>suppose </b></a><a NAME="E1:99_5_2"/><i><font color="Green" title="E77">A20</font></i>: 
<font color="Maroon" title="c9">t</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><span class="p1">(<span class="default"><font color="Maroon" title="c10">w</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c1">la</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-Chg</a> <font color="Maroon" title="c10">w</font>,<font color="Maroon" title="c3">a3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="ref" href="scmfsa_1.html#D7" title="SCMFSA_1:def.7">SCMFSA_1:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c3">a3</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T20" title="SCMFSA_1:th.20">SCMFSA_1:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c1">la</font></span>)</span>,<font color="Maroon" title="c9">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="txt" href="scmfsa_2.html#E1:99_5_2"><i><font color="Green" title="E77">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T7" target="_self" title="SCMFSA_2:th.7">Th7</a>, <a class="ref" href="scmfsa_2.html#T96" target="_self" title="SCMFSA_2:th.96">Th96</a></i>
<br/>.= 
<font color="Maroon" title="c9">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="txt" href="scmfsa_2.html#E22:99"><i><font color="Green" title="E76">A12</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>
;<br/><b>hence </b><a NAME="E3:99_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:99"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E5:99"><i><font color="Green" title="E67">A2</font></i></a>, <a class="txt" href="scmfsa_2.html#E10:99"><i><font color="Green" title="E70">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E21:99"><i><font color="Green" title="E75">A11</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
