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

<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="ami_1.html#V11" title="AMI_1:attr.11">autonomic</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:15"/>
 <a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E2:15"/><b>then </b><i><font color="Green" title="E10">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></i>;<br/>
<b>assume </b><a NAME="E3:15"/><i><font color="Green" title="E11">A2</font></i>: 
not  <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/>

<a NAME="E4:15"/>
not <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">autonomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c2">d1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E2:15_1"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">d1</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"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E2:15"><i><font color="Green" title="E10">A1</font></i></a></i>;<br/>
<a NAME="E3:15_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T37" title="AMI_3:th.37">AMI_3:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">d1</font> = <font color="Maroon" title="c2">d1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <b>by </b><i><a class="txt" href="scmpds_3.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a></i>;<br/>
<a NAME="E5:15_1"/>
 <a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="scmpds_3.html#T9" target="_self" title="SCMPDS_3:th.9">Th9</a></i>;<br/>
<a NAME="E6:15_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">d1</font> = <font color="Maroon" title="c3">d1</font> as    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  <b>by </b><i><a class="txt" href="scmpds_3.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="scmpds_2.html#T9" title="SCMPDS_2:th.9">SCMPDS_2:9</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">il</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <a href="subset_1.html#K7" title="SUBSET_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/>
<a NAME="E9:15_1"/>
not the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a>, <a class="ref" href="scmpds_2.html#T11" title="SCMPDS_2:th.11">SCMPDS_2:11</a></i>;<br/>
<a NAME="E10:15_1"/><b>then </b><i><font color="Green" title="E13">A4</font></i>: 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <a href="subset_1.html#K7" title="SUBSET_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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">il</font> = <font color="Maroon" title="c5">il</font> as   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">p1</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">p2</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c9">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="E13:15_1"/><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">s1</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39" title="AMI_3:th.39">AMI_3:39</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">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="E15:15_1"/><i><font color="Green" title="E15">A6</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">s2</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T39" title="AMI_3:th.39">AMI_3:39</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">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="c10">s2</font>
;<br/>

<a NAME="E16:15_1"/><i><font color="Green" title="E16">A7</font></i>: 
 <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#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </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#E3:15"><i><font color="Green" title="E11">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="E17:15_1"/>
not <font color="Maroon" title="c6">il</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>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E10:15_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E18:15_1"/><b>then </b><i><font color="Green" title="E17">A8</font></i>: 
 <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"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
 <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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> = 
<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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span></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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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/>.= 
<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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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><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/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>
;<br/>
<b>then </b><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#K3" title="XBOOLE_0:func.3">/\</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmpds_3.html#E16:15_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmpds_3.html#E18:15_1"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>
;<br/>
<a NAME="E21:15_1"/><b>then </b>
 <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>  <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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E22:15_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#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E23:15_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">s1</font>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E13:15_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>

 <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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> = 
<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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span></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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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/>.= 
<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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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><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/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>
;<br/>
<b>then </b><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#K3" title="XBOOLE_0:func.3">/\</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmpds_3.html#E16:15_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmpds_3.html#E18:15_1"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>
;<br/>
<a NAME="E26:15_1"/><b>then </b>
 <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>  <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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E27:15_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#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E28:15_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">s2</font>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E15:15_1"><i><font color="Green" title="E15">A6</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="E29:15_1"/>
 <a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <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>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E30:15_1"/><b>then </b><i><font color="Green" title="E18">A9</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/>
<a NAME="E31:15_1"/>
 <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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>;<br/>
<a NAME="E32:15_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T37" title="AMI_3:th.37">AMI_3:37</a></i>;<br/>
<a NAME="E33:15_1"/><b>then </b><i><font color="Green" title="E19">A10</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"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E34:15_1"/><i><font color="Green" title="E20">A11</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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><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="E35:15_1"/><b>then </b><i><font color="Green" title="E21">A12</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> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E36:15_1"/><i><font color="Green" title="E22">A13</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span></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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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="E37:15_1"/><b>then </b><i><font color="Green" title="E23">A14</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E35:15_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E38:15_1"/><i><font color="Green" title="E24">A15</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E39:15_1"/><b>then </b><i><font color="Green" title="E25">A16</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E37:15_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<i><font color="Green" title="E26">A17</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c9">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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#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#E13:15_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="scmpds_3.html#E39:15_1"><i><font color="Green" title="E25">A16</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</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#E37:15_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</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#E35:15_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<a NAME="E41:15_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</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"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E42:15_1"/><b>then </b><i><font color="Green" title="E27">A18</font></i>: 
<font color="Maroon" title="c6">il</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="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E43:15_1"/>
<font color="Maroon" title="c6">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/>
<a NAME="E44:15_1"/><b>then </b><i><font color="Green" title="E28">A19</font></i>: 
not <font color="Maroon" title="c6">il</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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E34:15_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E45:15_1"/><i><font color="Green" title="E29">A20</font></i>: 
<font color="Maroon" title="c6">il</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E36:15_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="txt" href="scmpds_3.html#E42:15_1"><i><font color="Green" title="E27">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E46:15_1"/><b>then </b>
<font color="Maroon" title="c6">il</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#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E38:15_1"><i><font color="Green" title="E24">A15</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="E30">A21</font></i>: <font color="Maroon" title="c9">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c6">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E13:15_1"><i><font color="Green" title="E14">A5</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E45:15_1"><i><font color="Green" title="E29">A20</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E44:15_1"><i><font color="Green" title="E28">A19</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 0
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<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#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scmpds_3.html#E40:15_1"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="scmpds_3.html#E47:15_1"><i><font color="Green" title="E30">A21</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E49:15_1"/><b>then </b><i><font color="Green" title="E31">A22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</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> <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="scmpds_3.html#E30:15_1"><i><font color="Green" title="E18">A9</font></i></a>, <a class="txt" href="scmpds_3.html#E33:15_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E50:15_1"/>
 <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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>;<br/>
<a NAME="E51:15_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T37" title="AMI_3:th.37">AMI_3:37</a></i>;<br/>
<a NAME="E52:15_1"/><b>then </b><i><font color="Green" title="E32">A23</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"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E53:15_1"/><i><font color="Green" title="E33">A24</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span></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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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="E54:15_1"/><b>then </b><i><font color="Green" title="E34">A25</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E35:15_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E55:15_1"/><i><font color="Green" title="E35">A26</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E56:15_1"/><b>then </b><i><font color="Green" title="E36">A27</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E54:15_1"><i><font color="Green" title="E34">A25</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<i><font color="Green" title="E37">A28</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c10">s2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></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#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#E15:15_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="scmpds_3.html#E56:15_1"><i><font color="Green" title="E36">A27</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</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#E54:15_1"><i><font color="Green" title="E34">A25</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</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#E35:15_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<a NAME="E58:15_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</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"><font color="Maroon" title="c6">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E59:15_1"/><b>then </b><i><font color="Green" title="E38">A29</font></i>: 
<font color="Maroon" title="c6">il</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="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E60:15_1"/>
<font color="Maroon" title="c6">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/>
<a NAME="E61:15_1"/><b>then </b><i><font color="Green" title="E39">A30</font></i>: 
not <font color="Maroon" title="c6">il</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"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E34:15_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E62:15_1"/><i><font color="Green" title="E40">A31</font></i>: 
<font color="Maroon" title="c6">il</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E53:15_1"><i><font color="Green" title="E33">A24</font></i></a>, <a class="txt" href="scmpds_3.html#E59:15_1"><i><font color="Green" title="E38">A29</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E63:15_1"/><b>then </b>
<font color="Maroon" title="c6">il</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#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_3.html#E55:15_1"><i><font color="Green" title="E35">A26</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="E41">A32</font></i>: <font color="Maroon" title="c10">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c6">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E15:15_1"><i><font color="Green" title="E15">A6</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"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c6">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E62:15_1"><i><font color="Green" title="E40">A31</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">il</font> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">il</font>
<b>by </b><i><a class="txt" href="scmpds_3.html#E61:15_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c4">d1</font> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 1
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<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#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="scmpds_3.html#E57:15_1"><i><font color="Green" title="E37">A28</font></i></a>, <a class="txt" href="scmpds_3.html#E64:15_1"><i><font color="Green" title="E41">A32</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/>
<b>hence </b><a NAME="E66:15_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c10">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="scmpds_3.html#E30:15_1"><i><font color="Green" title="E18">A9</font></i></a>, <a class="txt" href="scmpds_3.html#E49:15_1"><i><font color="Green" title="E31">A22</font></i></a>, <a class="txt" href="scmpds_3.html#E52:15_1"><i><font color="Green" title="E32">A23</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:15"/>
contradiction
 ;<br/>


</div>
