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

<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 ;<br/>

<b>assume </b><a NAME="E2:41"/><i><font color="Green" title="E28">A2</font></i>: 
not  <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</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> <font color="Maroon" title="c1">p</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c2">il</font> =  <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font>;<br/>
<b>set </b><font color="Maroon" title="c3">p1</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">p2</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c5">s1</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E4:41"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T82" title="AMI_1:th.82">AMI_1:82</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">s2</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E6:41"/><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T82" title="AMI_1:th.82">AMI_1:82</a></i>;<br/>
<a NAME="E7:41"/>
not <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>proof </b></a><div class="add">

<a NAME="E1:41_1"/><i><font color="Green" title="E31">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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="E2:41_1"/><i><font color="Green" title="E32">A6</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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/>
<b>take </b>
<font color="Maroon" title="c5">s1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a><br/>

<b>take </b>
<font color="Maroon" title="c6">s2</font>
;<br/>

<a NAME="E3:41_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:41"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E4:41_1"/><b>then </b>
( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:41_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="txt" href="ami_5.html#E2:41_1"><i><font color="Green" title="E32">A6</font></i></a>, <a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E5:41_1"/><i><font color="Green" title="E33">A7</font></i>: 
( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s2</font> )
 <b>by </b><i><a class="txt" href="ami_5.html#E4:41"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="ami_5.html#E6:41"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>

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

<a NAME="E6:41_1"/><i><font color="Green" title="E34">A8</font></i>: 
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</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"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:41_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:41_1"/><i><font color="Green" title="E35">A9</font></i>: 
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</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"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:41_1"><i><font color="Green" title="E32">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:41_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></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 NAME="E9:41_1"/><b>then </b>
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</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"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E7:41_1"><i><font color="Green" title="E35">A9</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E36">A10</font></i>: <font color="Maroon" title="c5">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></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#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E4:41"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></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#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E7:41_1"><i><font color="Green" title="E35">A9</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<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="E11:41_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</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"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></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 NAME="E12:41_1"/><b>then </b>
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</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"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E6:41_1"><i><font color="Green" title="E34">A8</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E37">A11</font></i>: <font color="Maroon" title="c6">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></span>)</span></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#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E6:41"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span></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#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E6:41_1"><i><font color="Green" title="E34">A8</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<i><font color="Green" title="E38">A12</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c5">s1</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
<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"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="ami_5.html#E5:41_1"><i><font color="Green" title="E33">A7</font></i></a>, <a class="txt" href="ami_5.html#E10:41_1"><i><font color="Green" title="E36">A10</font></i></a>, <a class="ref" href="ami_1.html#T97" title="AMI_1:th.97">AMI_1:97</a></i>
<br/>.= 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
;<br/>
<i><font color="Green" title="E39">A13</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c6">s2</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
<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"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c6">s2</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="ami_5.html#E5:41_1"><i><font color="Green" title="E33">A7</font></i></a>, <a class="txt" href="ami_5.html#E13:41_1"><i><font color="Green" title="E37">A11</font></i></a>, <a class="ref" href="ami_1.html#T97" title="AMI_1:th.97">AMI_1:97</a></i>
<br/>.= 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1
<b>by </b><i><a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
;<br/>
<b>assume </b><a NAME="E16:41_1"/><i><font color="Green" title="E40">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
 ;<br/>

<i><font color="Green" title="E41">A15</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E16:41_1"><i><font color="Green" title="E40">A14</font></i></a>, <a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
;<br/>
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="ami_5.html#E14:41_1"><i><font color="Green" title="E38">A12</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1
<b>by </b><i><a class="txt" href="ami_5.html#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="ami_5.html#E15:41_1"><i><font color="Green" title="E39">A13</font></i></a>, <a class="txt" href="ami_5.html#E17:41_1"><i><font color="Green" title="E41">A15</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>
<b>hence </b><a NAME="E19:41_1"/>
contradiction
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:41"/>
contradiction
 ;<br/>


</div>
