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

<span class="kw">let </span><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#NM4" title="AMI_1:NM.4">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K24" title="AMI_1:func.24">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/>

<span class="kw">assume </span><a NAME="E1:81"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:81"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">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/>
<span class="kw">assume </span><a NAME="E3:81"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:81"/>
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="81_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:81_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:81"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E2:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">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/>
<span class="kw">consider </span><font color="Maroon" title="c3">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/>
<span class="kw">consider </span><font color="Maroon" title="c4">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#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E6:81_1"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c4">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#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:81"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<a NAME="E7:81_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#K24" title="AMI_1:func.24">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">d1</font> = <font color="Maroon" title="c4">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a></span>;<br/>
<a NAME="E9:81_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="E10:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></span>;<br/>
<a NAME="E11:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">d2</font> = <font color="Maroon" title="c3">d2</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></span>;<br/>
<a NAME="E13:81_1"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E14:81_1"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E15:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E16:81_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="E17:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></span>;<br/>
<a NAME="E18:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">il</font> = <font color="Maroon" title="c2">il</font> as    <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>  ;<br/>
<a NAME="E20:81_1"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
not <font color="Maroon" title="c7">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:81_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E21:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E22:81_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#K24" title="AMI_1:func.24">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> 
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">d1</font> = <font color="Maroon" title="c5">d1</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></span>;<br/>
<a NAME="E24:81_1"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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="c7">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="c8">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#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">p2</font> = <font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">p1</font> = <font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>;<br/>
<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E26:81_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T156" title="PBOOLE:th.156">PBOOLE:156</a></span>;<br/>
<a NAME="E27:81_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:81_1"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E28:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A13</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E29:81_1"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E31:81_1"/><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T156" title="PBOOLE:th.156">PBOOLE:156</a></span>;<br/>
<a NAME="E32:81_1"/><span class="lab"><font color="Green" title="E33">X</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<a NAME="E33:81_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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E34:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A16</font></span>: 
 <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">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:81_1"><span class="lab"><font color="Green" title="E33">X</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E35:81_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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E36:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A17</font></span>: 
 <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">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:81_1"><span class="lab"><font color="Green" title="E33">X</font></span></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></span>;<br/>
<a NAME="E37:81_1"/><span class="lab"><font color="Green" title="E36">A18</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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="c7">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="c8">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#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E38:81_1"/><span class="lab"><font color="Green" title="E37">A19</font></span>: 
 <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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:81_1"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E39:81_1"/><span class="lab"><font color="Green" title="E38">A20</font></span>: 
 <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E40:81_1"/><span class="lab"><font color="Green" title="E39">A21</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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"><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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E41:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A22</font></span>: 
 <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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E42:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A23</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:81_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E43:81_1"/><span class="kw">then </span>
 <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:81_1"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E42">A24</font></span>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c12">s2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:81_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:81_1"><span class="lab"><font color="Green" title="E41">A23</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:81_1"><span class="lab"><font color="Green" title="E40">A22</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E45:81_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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T20" target="_self" title="AMI_5:th.20">Th20</a></span>;<br/>
<a NAME="E46:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A25</font></span>: 
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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:81_1"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E47:81_1"/><span class="lab"><font color="Green" title="E44">A26</font></span>: 
 <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#K12" title="AMI_3:func.12">.--&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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E48:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A27</font></span>: 
<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#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E49:81_1"/><span class="kw">then </span>
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:81_1"><span class="lab"><font color="Green" title="E36">A18</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E50:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A28</font></span>: 
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:81_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E51:81_1"/><span class="kw">then </span>
<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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:81_1"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E47">A29</font></span>: <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:81_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:81_1"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:81_1"><span class="lab"><font color="Green" title="E43">A25</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:81_1"><span class="lab"><font color="Green" title="E45">A27</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E53:81_1"/>
<font color="Maroon" title="c7">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></span>;<br/>
<a NAME="E54:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A30</font></span>: 
not <font color="Maroon" title="c7">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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:81_1"><span class="lab"><font color="Green" title="E39">A21</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E55:81_1"/>
<font color="Maroon" title="c7">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T22" target="_self" title="AMI_5:th.22">Th22</a></span>;<br/>
<a NAME="E56:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A31</font></span>: 
not <font color="Maroon" title="c7">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#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:81_1"><span class="lab"><font color="Green" title="E44">A26</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E57:81_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">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="c8">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E58:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="c7">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="c8">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 class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E59:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:81_1"><span class="lab"><font color="Green" title="E36">A18</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E60:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A32</font></span>: 
<font color="Maroon" title="c7">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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:81_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E61:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:81_1"><span class="lab"><font color="Green" title="E38">A20</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E51">A33</font></span>: <font color="Maroon" title="c12">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:81_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:81_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:81_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">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="c8">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="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:81_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<font color="Maroon" title="c8">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E63:81_1"/><span class="lab"><font color="Green" title="E52">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c12">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c12">s2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<span class="lab"><font color="Green" title="E53">A34</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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="c8">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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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="c8">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
<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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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="c8">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:81_1"><span class="lab"><font color="Green" title="E42">A24</font></span></a>, <a class="txt" href="#E62:81_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E52:81_1"><span class="lab"><font color="Green" title="E47">A29</font></span></a>, <a class="txt" href="#E63:81_1"><span class="lab"><font color="Green" title="E52">Y</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
;<br/>
<a NAME="E65:81_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:81"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<a NAME="E66:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A35</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E67:81_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E68:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A36</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">s1</font>
; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">K98</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c12">s2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">K98</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<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="c7">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="c8">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#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
;<br/>
<span class="kw">then </span><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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:81_1"><span class="lab"><font color="Green" title="E54">A35</font></span></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>
<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="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:81_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:81_1"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>
;<br/>
<a NAME="E71:81_1"/><span class="kw">then </span>
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E72:81_1"/><span class="kw">then </span>
<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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E73:81_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:81_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">K98</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<a NAME="E74:81_1"/><span class="lab"><font color="Green" title="E56">A37</font></span>: 
 <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<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="c7">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="c8">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#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
;<br/>
<span class="kw">then </span><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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:81_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>
<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="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:81_1"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:81_1"><span class="lab"><font color="Green" title="E37">A19</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>
;<br/>
<a NAME="E77:81_1"/><span class="kw">then </span>
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E78:81_1"/><span class="kw">then </span>
<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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E79:81_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:81_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">K98</a>() holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<span class="kw">take </span>
1
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<a NAME="E80:81_1"/><span class="lab"><font color="Green" title="E57">A38</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E81:81_1"/><span class="lab"><font color="Green" title="E58">A39</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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"><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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E82:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A40</font></span>: 
 <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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E83:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A41</font></span>: 
 <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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:81_1"><span class="lab"><font color="Green" title="E57">A38</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E84:81_1"/><span class="kw">then </span>
 <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:81_1"><span class="lab"><font color="Green" title="E56">A37</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E61">A42</font></span>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c11">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:81_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E83:81_1"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:81_1"><span class="lab"><font color="Green" title="E59">A40</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E86:81_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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T20" target="_self" title="AMI_5:th.20">Th20</a></span>;<br/>
<a NAME="E87:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A43</font></span>: 
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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E81:81_1"><span class="lab"><font color="Green" title="E58">A39</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E88:81_1"/><span class="lab"><font color="Green" title="E63">A44</font></span>: 
 <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#K12" title="AMI_3:func.12">.--&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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E89:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A45</font></span>: 
<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#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E90:81_1"/><span class="kw">then </span>
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:81_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E91:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A46</font></span>: 
<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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:81_1"><span class="lab"><font color="Green" title="E57">A38</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E92:81_1"/><span class="kw">then </span>
<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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:81_1"><span class="lab"><font color="Green" title="E56">A37</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E66">A47</font></span>: <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:81_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E91:81_1"><span class="lab"><font color="Green" title="E65">A46</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E87:81_1"><span class="lab"><font color="Green" title="E62">A43</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E89:81_1"><span class="lab"><font color="Green" title="E64">A45</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E94:81_1"/>
<font color="Maroon" title="c7">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></span>;<br/>
<a NAME="E95:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A48</font></span>: 
not <font color="Maroon" title="c7">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#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E81:81_1"><span class="lab"><font color="Green" title="E58">A39</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E96:81_1"/>
<font color="Maroon" title="c7">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_5.html#T22" target="_self" title="AMI_5:th.22">Th22</a></span>;<br/>
<a NAME="E97:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A49</font></span>: 
not <font color="Maroon" title="c7">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#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E88:81_1"><span class="lab"><font color="Green" title="E63">A44</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E98:81_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">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="c8">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E99:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="c7">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="c8">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 class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E100:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:81_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E101:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A50</font></span>: 
<font color="Maroon" title="c7">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="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:81_1"><span class="lab"><font color="Green" title="E57">A38</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E102:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:81_1"><span class="lab"><font color="Green" title="E56">A37</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E70">A51</font></span>: <font color="Maroon" title="c11">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c7">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:81_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <font color="Maroon" title="c7">il</font>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E101:81_1"><span class="lab"><font color="Green" title="E69">A50</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">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="c8">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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">d2</font> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&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="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E95:81_1"><span class="lab"><font color="Green" title="E67">A48</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">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="c8">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="c7">il</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E97:81_1"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<font color="Maroon" title="c8">d1</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c6">d2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/>
<a NAME="E104:81_1"/><span class="lab"><font color="Green" title="E71">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c11">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c11">s1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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="c8">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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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="c8">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
<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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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="c8">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:81_1"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="txt" href="#E103:81_1"><span class="lab"><font color="Green" title="E70">A51</font></span></a>, <a class="txt" href="#E93:81_1"><span class="lab"><font color="Green" title="E66">A47</font></span></a>, <a class="txt" href="#E104:81_1"><span class="lab"><font color="Green" title="E71">Y</font></span></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></span>
;<br/>
<a NAME="E106:81_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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="c8">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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E68:81_1"><span class="lab"><font color="Green" title="E55">A36</font></span></a>, <a class="txt" href="#E36:81_1"><span class="lab"><font color="Green" title="E35">A17</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E107:81_1"/>
not <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c11">s1</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s2</font></span>)</span>,<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#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E68:81_1"><span class="lab"><font color="Green" title="E55">A36</font></span></a>, <a class="txt" href="#E34:81_1"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="txt" href="#E64:81_1"><span class="lab"><font color="Green" title="E53">A34</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:81"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
