<?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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E12">A1</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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="E2:20"/><i><font color="Green" title="E13">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E4:20"/><i><font color="Green" title="E14">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E6:20"/><i><font color="Green" title="E15">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="E7:20"/>
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="20_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1"/><i><font color="Green" title="E16">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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"><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="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E2:20_1"/><i><font color="Green" title="E17">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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"><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="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</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="E3:20_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="tarski.html#K1" title="TARSKI:func.1">{</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="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E2:20"><i><font color="Green" title="E13">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="E4:20_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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="scmpds_3.html#E2:20_1"><i><font color="Green" title="E17">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="E5:20_1"/><i><font color="Green" title="E18">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="scmpds_3.html#E4:20"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="scmpds_3.html#E6:20"><i><font color="Green" title="E15">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="E6:20_1"/><i><font color="Green" title="E19">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:20_1"/><i><font color="Green" title="E20">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E2:20_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:20_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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</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">(<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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="E9:20_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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</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="scmpds_3.html#E7:20_1"><i><font color="Green" title="E20">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="E21">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</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="scmpds_3.html#E4:20"><i><font color="Green" title="E14">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="scmpds_3.html#E7:20_1"><i><font color="Green" title="E20">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E11:20_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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="E12:20_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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E6:20_1"><i><font color="Green" title="E19">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="E22">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</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="scmpds_3.html#E6:20"><i><font color="Green" title="E15">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="scmpds_3.html#E6:20_1"><i><font color="Green" title="E19">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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<i><font color="Green" title="E23">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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E5:20_1"><i><font color="Green" title="E18">A7</font></i></a>, <a class="txt" href="scmpds_3.html#E10:20_1"><i><font color="Green" title="E21">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="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c5">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/>
<i><font color="Green" title="E24">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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 1</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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E5:20_1"><i><font color="Green" title="E18">A7</font></i></a>, <a class="txt" href="scmpds_3.html#E13:20_1"><i><font color="Green" title="E22">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="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c6">s2</font>,1
<b>by </b><i><a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/>
<b>assume </b><a NAME="E16:20_1"/><i><font color="Green" title="E25">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="E26">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="scmpds_3.html#E16:20_1"><i><font color="Green" title="E25">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/>
<i><font color="Green" title="E27">A16</font></i>:  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c5">s1</font>,<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="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E14:20_1"><i><font color="Green" title="E23">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="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c6">s2</font>,1
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E15:20_1"><i><font color="Green" title="E24">A13</font></i></a>, <a class="txt" href="scmpds_3.html#E17:20_1"><i><font color="Green" title="E26">A15</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_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font> = 
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E5:20_1"><i><font color="Green" title="E18">A7</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_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E5:20_1"><i><font color="Green" title="E18">A7</font></i></a>, <a class="ref" href="ami_1.html#T97" title="AMI_1:th.97">AMI_1:97</a></i>
;<br/>
<b>hence </b><a NAME="E20:20_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_3.html#E18:20_1"><i><font color="Green" title="E27">A16</font></i></a>, <a class="ref" href="scmpds_3.html#T19" target="_self" title="SCMPDS_3:th.19">Th19</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:20"/>
contradiction
 ;<br/>


</div>
