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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="ami_1.html#V11">autonomic</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green">E34</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:49"/><i><font color="Green">E35</font></i>: 
not  <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:49"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39">AMI_3:39</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:49"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39">AMI_3:39</a></i>;<br/>
<a NAME="E7:49"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V11">autonomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<a NAME="E1:49_1"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E2:49_1"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25">AMI_1:def 25</a><br/>

<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E3:49_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:49_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="scmring4.html#E2:49"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>


</div><b>end;</b></div>
<a NAME="E4:49_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:49_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmring4.html#E2:49_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E5:49_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="scmring4.html#E4:49"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmring4.html#E6:49"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>

<b>take </b>
1
;<br/>

<a NAME="E6:49_1"/><i><font color="Green">E41</font></i>: 
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:49_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:49_1"/><i><font color="Green">E42</font></i>: 
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:49_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:49_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E9:49_1"/><b>then </b>
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font> <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="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E7:49_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E43</font></i>: <font color="Maroon">c<sub>6</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E4:49"><i><font color="Green">E36</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E7:49_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmring2.html#K9">goto</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/>
<a NAME="E11:49_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E12:49_1"/><b>then </b>
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font> <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="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E6:49_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E44</font></i>: <font color="Maroon">c<sub>7</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p5">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E6:49"><i><font color="Green">E37</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E6:49_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmring2.html#K9">goto</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/>
<i><font color="Green">E45</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0</span>)</span></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmring4.html#E5:49_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmring4.html#E10:49_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0
<b>by </b><i><a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
;<br/>
<i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="ami_1.html#K13">.</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmring4.html#E5:49_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmring4.html#E13:49_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="ami_5.html#T60">AMI_5:60</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
<b>by </b><i><a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
;<br/>
<b>assume </b><a NAME="E16:49_1"/><i><font color="Green">E47</font></i>: 
<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>6</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</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>7</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<i><font color="Green">E48</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</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>6</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<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>6</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</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>7</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E16:49_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/>
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,0 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E1:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmring4.html#E14:49_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
<b>by </b><i><a class="txt" href="scmring4.html#E1:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmring4.html#E15:49_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmring4.html#E17:49_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<b>hence </b><a NAME="E19:49_1"/>
contradiction
 <b>by </b><i><a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:49"/>
contradiction
 ;<br/>


</div>
