<?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#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K35" title="AMI_1:func.35">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>  implies  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> )</span><br/>

<b>assume </b><a NAME="E1:30"/>
 <a href="ami_1.html#K35" title="AMI_1:func.35">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span><br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">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> 
 
;<br/>
<b>assume </b><a NAME="E3:30"/><i><font color="Green" title="E20">A2</font></i>: 
not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:30"/>
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="30_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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E2:30_1"/><i><font color="Green" title="E21">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:30"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/>
<a NAME="E3:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="txt" href="#E2:30_1"><i><font color="Green" title="E21">A3</font></i></a></i>;<br/>
<a NAME="E5:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">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="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a>, <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="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="#E2:30_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">d2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E8:30_1"/>
not  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
;<br/>
<a NAME="E9:30_1"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
<a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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/>
<a NAME="E10:30_1"/><b>then </b>
<font color="Maroon" title="c5">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">d2</font> = <font color="Maroon" title="c5">d2</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">il</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E13:30_1"/>
not  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
;<br/>
<a NAME="E14:30_1"/><b>then </b><i><font color="Green" title="E23">A5</font></i>: 
<a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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/>
<a NAME="E15:30_1"/><b>then </b>
<font color="Maroon" title="c7">il</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">il</font> = <font color="Maroon" title="c7">il</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">p1</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">p2</font> = <font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c11">s1</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E18:30_1"/><i><font color="Green" title="E24">A6</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">s1</font>
 <b>by </b><i><a class="ref" href="card_3.html#T97" title="CARD_3:th.97">CARD_3:97</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">s2</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E20:30_1"/><i><font color="Green" title="E25">A7</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s2</font>
 <b>by </b><i><a class="ref" href="card_3.html#T97" title="CARD_3:th.97">CARD_3:97</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c11">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="card_3.html#K4" title="CARD_3:func.4">K242</a>(the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ) st <br/>( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; not for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">K97</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<font color="Olive">b<sub>2</sub></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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<b>take </b>
<font color="Maroon" title="c12">s2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">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="c12">s2</font> &amp; not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">K97</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<a NAME="E21:30_1"/><i><font color="Green" title="E26">A8</font></i>: 
not <font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="txt" href="#E9:30_1"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E22:30_1"/><i><font color="Green" title="E27">A9</font></i>: 
not <font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="txt" href="#E14:30_1"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E23:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E3:30"><i><font color="Green" title="E20">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="E24:30_1"/><b>then </b><i><font color="Green" title="E28">A10</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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"><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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<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="E25:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E21:30_1"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E26:30_1"/><b>then </b><i><font color="Green" title="E29">A11</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<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="E27:30_1"/><i><font color="Green" title="E30">A12</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="c8">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E22:30_1"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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="ami_3.html#K1" title="AMI_3:func.1">SCM</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">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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="ami_3.html#K1" title="AMI_3:func.1">SCM</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">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</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"><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="ami_3.html#K1" title="AMI_3:func.1">SCM</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/>
<b>then </b><span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">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">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</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="#E24:30_1"><i><font color="Green" title="E28">A10</font></i></a>, <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#NK2" title="RELAT_1:NK.2">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="c8">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="#E26:30_1"><i><font color="Green" title="E29">A11</font></i></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="#E27:30_1"><i><font color="Green" title="E30">A12</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="E30:30_1"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E31:30_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#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E32:30_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">s1</font>
 <b>by </b><i><a class="txt" href="#E18:30_1"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s2</font> &amp; not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">K97</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<a NAME="E33:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E3:30"><i><font color="Green" title="E20">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="E34:30_1"/><b>then </b><i><font color="Green" title="E31">A13</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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"><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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<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="E35:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E21:30_1"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E36:30_1"/><b>then </b><i><font color="Green" title="E32">A14</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<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="E37:30_1"/><i><font color="Green" title="E33">A15</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="c8">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E22:30_1"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</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="ami_3.html#K1" title="AMI_3:func.1">SCM</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">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</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="ami_3.html#K1" title="AMI_3:func.1">SCM</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">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</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"><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="ami_3.html#K1" title="AMI_3:func.1">SCM</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/>
<b>then </b><span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">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">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">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="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">d2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</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="#E34:30_1"><i><font color="Green" title="E31">A13</font></i></a>, <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#NK2" title="RELAT_1:NK.2">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="c8">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="#E36:30_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="#E37:30_1"><i><font color="Green" title="E33">A15</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="E40:30_1"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E41:30_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#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E42:30_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s2</font>
 <b>by </b><i><a class="txt" href="#E20:30_1"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">K97</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,<font color="Olive">b<sub>1</sub></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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<b>take </b>
1
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<a NAME="E43:30_1"/>
 <a href="ami_1.html#K35" title="AMI_1:func.35">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="E44:30_1"/><b>then </b><i><font color="Green" title="E34">A16</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">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#NK2" title="RELAT_1:NK.2">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="E45:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E46:30_1"/><b>then </b><i><font color="Green" title="E35">A17</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="c11">s1</font>,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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E47:30_1"/><i><font color="Green" title="E36">A18</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="E48:30_1"/><b>then </b><i><font color="Green" title="E37">A19</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E49:30_1"/><i><font color="Green" title="E38">A20</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E50:30_1"/><b>then </b><i><font color="Green" title="E39">A21</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E48:30_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E51:30_1"/><i><font color="Green" title="E40">A22</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E52:30_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E50:30_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E41">A23</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c11">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E18:30_1"><i><font color="Green" title="E24">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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E50:30_1"><i><font color="Green" title="E39">A21</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_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E48:30_1"><i><font color="Green" title="E37">A19</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="c8">il</font>
<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="E54:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">il</font></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="E55:30_1"/><b>then </b><i><font color="Green" title="E42">A24</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E56:30_1"/><i><font color="Green" title="E43">A25</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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">d2</font></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="E57:30_1"/>
<font color="Maroon" title="c8">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d2</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self" title="AMI_5:th.22">Th22</a></i>;<br/>
<a NAME="E58:30_1"/><b>then </b><i><font color="Green" title="E44">A26</font></i>: 
not <font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E56:30_1"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E59:30_1"/><i><font color="Green" title="E45">A27</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </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="E60:30_1"/><b>then </b><i><font color="Green" title="E46">A28</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E55:30_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E61:30_1"/>
<font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="E62:30_1"/><b>then </b><i><font color="Green" title="E47">A29</font></i>: 
not <font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E47:30_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E63:30_1"/><i><font color="Green" title="E48">A30</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E49:30_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="#E60:30_1"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E64:30_1"/><b>then </b>
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E51:30_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E49">A31</font></i>: <font color="Maroon" title="c11">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E18:30_1"><i><font color="Green" title="E24">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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E63:30_1"><i><font color="Green" title="E48">A30</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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E62:30_1"><i><font color="Green" title="E47">A29</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E58:30_1"><i><font color="Green" title="E44">A26</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="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font>
<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="E66:30_1"/><i><font color="Green" title="E50">A32</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E56:30_1"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E67:30_1"/><b>then </b><i><font color="Green" title="E51">A33</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E59:30_1"><i><font color="Green" title="E45">A27</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E68:30_1"/>
<font color="Maroon" title="c6">d2</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T20" target="_self" title="AMI_5:th.20">Th20</a></i>;<br/>
<a NAME="E69:30_1"/><b>then </b><i><font color="Green" title="E52">A34</font></i>: 
not <font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E47:30_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E70:30_1"/><i><font color="Green" title="E53">A35</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E49:30_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="#E67:30_1"><i><font color="Green" title="E51">A33</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E71:30_1"/><b>then </b>
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E51:30_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E54">A36</font></i>: <font color="Maroon" title="c11">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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">d2</font>
<b>by </b><i><a class="txt" href="#E18:30_1"><i><font color="Green" title="E24">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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E70:30_1"><i><font color="Green" title="E53">A35</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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E69:30_1"><i><font color="Green" title="E52">A34</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E66:30_1"><i><font color="Green" title="E50">A32</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="card_1.html#NK1" title="CARD_1:NK.1">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/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<span class="p2">(<span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3: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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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="c11">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
<br/>.= 
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
<b>by </b><i><a class="txt" href="#E53:30_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="#E65:30_1"><i><font color="Green" title="E49">A31</font></i></a>, <a class="txt" href="#E72:30_1"><i><font color="Green" title="E54">A36</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
;<br/>
<a NAME="E74:30_1"/><b>then </b><i><font color="Green" title="E55">A37</font></i>: 
<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="c11">s1</font>,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#NK2" title="RELAT_1:NK.2">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>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<b>by </b><i><a class="txt" href="#E2:30_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="#E44:30_1"><i><font color="Green" title="E34">A16</font></i></a>, <a class="txt" href="#E46:30_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E75:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E76:30_1"/><b>then </b><i><font color="Green" title="E56">A38</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">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="c12">s2</font>,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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E77:30_1"/><i><font color="Green" title="E57">A39</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="E78:30_1"/><b>then </b><i><font color="Green" title="E58">A40</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E79:30_1"/><i><font color="Green" title="E59">A41</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E80:30_1"/><b>then </b><i><font color="Green" title="E60">A42</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E78:30_1"><i><font color="Green" title="E58">A40</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E81:30_1"/><i><font color="Green" title="E61">A43</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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#NK2" title="RELAT_1:NK.2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="E82:30_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E80:30_1"><i><font color="Green" title="E60">A42</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E62">A44</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c12">s2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E20:30_1"><i><font color="Green" title="E25">A7</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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E80:30_1"><i><font color="Green" title="E60">A42</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_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E78:30_1"><i><font color="Green" title="E58">A40</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="c8">il</font>
<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="E84:30_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">il</font></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="E85:30_1"/><b>then </b><i><font color="Green" title="E63">A45</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E86:30_1"/><i><font color="Green" title="E64">A46</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</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">d2</font></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="E87:30_1"/>
<font color="Maroon" title="c8">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d2</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self" title="AMI_5:th.22">Th22</a></i>;<br/>
<a NAME="E88:30_1"/><b>then </b><i><font color="Green" title="E65">A47</font></i>: 
not <font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="#E86:30_1"><i><font color="Green" title="E64">A46</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E89:30_1"/><i><font color="Green" title="E66">A48</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</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="E90:30_1"/><b>then </b><i><font color="Green" title="E67">A49</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E85:30_1"><i><font color="Green" title="E63">A45</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E91:30_1"/>
<font color="Maroon" title="c8">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="E92:30_1"/><b>then </b><i><font color="Green" title="E68">A50</font></i>: 
not <font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E77:30_1"><i><font color="Green" title="E57">A39</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E93:30_1"/><i><font color="Green" title="E69">A51</font></i>: 
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E79:30_1"><i><font color="Green" title="E59">A41</font></i></a>, <a class="txt" href="#E90:30_1"><i><font color="Green" title="E67">A49</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E94:30_1"/><b>then </b>
<font color="Maroon" title="c8">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E81:30_1"><i><font color="Green" title="E61">A43</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E70">A52</font></i>: <font color="Maroon" title="c12">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c8">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E20:30_1"><i><font color="Green" title="E25">A7</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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E93:30_1"><i><font color="Green" title="E69">A51</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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E92:30_1"><i><font color="Green" title="E68">A50</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">il</font>
<b>by </b><i><a class="txt" href="#E88:30_1"><i><font color="Green" title="E65">A47</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="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font>
<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="E96:30_1"/><i><font color="Green" title="E71">A53</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="#E86:30_1"><i><font color="Green" title="E64">A46</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E97:30_1"/><b>then </b><i><font color="Green" title="E72">A54</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E89:30_1"><i><font color="Green" title="E66">A48</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E98:30_1"/>
<font color="Maroon" title="c6">d2</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T20" target="_self" title="AMI_5:th.20">Th20</a></i>;<br/>
<a NAME="E99:30_1"/><b>then </b><i><font color="Green" title="E73">A55</font></i>: 
not <font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E77:30_1"><i><font color="Green" title="E57">A39</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E100:30_1"/><i><font color="Green" title="E74">A56</font></i>: 
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E79:30_1"><i><font color="Green" title="E59">A41</font></i></a>, <a class="txt" href="#E97:30_1"><i><font color="Green" title="E72">A54</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E101:30_1"/><b>then </b>
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E81:30_1"><i><font color="Green" title="E61">A43</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then </b><i><font color="Green" title="E75">A57</font></i>: <font color="Maroon" title="c12">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">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">d2</font>
<b>by </b><i><a class="txt" href="#E20:30_1"><i><font color="Green" title="E25">A7</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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <font color="Maroon" title="c8">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E100:30_1"><i><font color="Green" title="E74">A56</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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">il</font> <a href="ami_4.html#K1" title="AMI_4:func.1">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E99:30_1"><i><font color="Green" title="E73">A55</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<b>by </b><i><a class="txt" href="#E96:30_1"><i><font color="Green" title="E71">A53</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,<span class="p2">(<span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3: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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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="c12">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="#E83:30_1"><i><font color="Green" title="E62">A44</font></i></a>, <a class="txt" href="#E95:30_1"><i><font color="Green" title="E70">A52</font></i></a>, <a class="txt" href="#E102:30_1"><i><font color="Green" title="E75">A57</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
;<br/>
<b>hence </b><a NAME="E104:30_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c11">s1</font>,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#NK2" title="RELAT_1:NK.2">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c12">s2</font>,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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:30_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="#E44:30_1"><i><font color="Green" title="E34">A16</font></i></a>, <a class="txt" href="#E74:30_1"><i><font color="Green" title="E55">A37</font></i></a>, <a class="txt" href="#E76:30_1"><i><font color="Green" title="E56">A38</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:30"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
