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

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E32">A1</font></i>: 
not <font color="Maroon" title="c1">R</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">p</font> be  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:45"/>
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E3:45"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></i>;<br/>
<b>assume </b><a NAME="E4:45"/><i><font color="Green" title="E34">A3</font></i>: 
not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 ;<br/>

<a NAME="E5:45"/>
not <font color="Maroon" title="c2">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="45_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c3">d1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span>;<br/>
<a NAME="E2:45_1"/><i><font color="Green" title="E35">A4</font></i>: 
<font color="Maroon" title="c3">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E3:45"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/>
<a NAME="E3:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">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 <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">d1</font> = <font color="Maroon" title="c3">d1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <b>by </b><i><a class="txt" href="scmring4.html#E2:45_1"><i><font color="Green" title="E35">A4</font></i></a></i>;<br/>
<a NAME="E5:45_1"/>
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="scmring4.html#T24" target="_self" title="SCMRING4:th.24">Th24</a></i>;<br/>
<a NAME="E6:45_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">d1</font> = <font color="Maroon" title="c4">d1</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="scmring4.html#E2:45_1"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">d2</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">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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span>;<br/>
<a NAME="E9:45_1"/>
not  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>
<a NAME="E10:45_1"/><b>then </b><i><font color="Green" title="E36">A5</font></i>: 
<a href="ami_2.html#K5" title="AMI_2:func.5">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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/>
<a NAME="E11:45_1"/><b>then </b>
<font color="Maroon" title="c6">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">d2</font> = <font color="Maroon" title="c6">d2</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">il</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span>;<br/>
<a NAME="E14:45_1"/>
not the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>
<a NAME="E15:45_1"/><b>then </b><i><font color="Green" title="E37">A6</font></i>: 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/>
<a NAME="E16:45_1"/><b>then </b>
<font color="Maroon" title="c8">il</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">il</font> = <font color="Maroon" title="c8">il</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E19:45_1"/><i><font color="Green" title="E38">A7</font></i>: 
<font color="Maroon" title="c10">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:45"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="anproj_1.html#D8" title="ANPROJ_1:def.8">ANPROJ_1:def 8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">p1</font> = <font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">p2</font> = <font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c13">s1</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E21:45_1"/><i><font color="Green" title="E39">A8</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">s1</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T82" title="AMI_1:th.82">AMI_1:82</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">s2</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E23:45_1"/><i><font color="Green" title="E40">A9</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">s2</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T82" title="AMI_1:th.82">AMI_1:82</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c13">s1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a><br/>

<b>take </b>
<font color="Maroon" title="c14">s2</font>
;<br/>

<a NAME="E24:45_1"/><i><font color="Green" title="E41">A10</font></i>: 
not <font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E10:45_1"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E25:45_1"/><i><font color="Green" title="E42">A11</font></i>: 
not <font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E15:45_1"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E26:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1"><b>proof </b></a><div class="add">

 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">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#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</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> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmring4.html#E4:45"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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> 
<b>by </b><i><a class="txt" href="scmring4.html#E24:45_1"><i><font color="Green" title="E41">A10</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmring4.html#E25:45_1"><i><font color="Green" title="E42">A11</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a><br/>


</div><b>end;</b></div>
<a NAME="E27:45_1"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E28:45_1"/>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">s1</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E21:45_1"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>

<a NAME="E29:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_2"><b>proof </b></a><div class="add">

 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</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#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">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#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</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> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c7">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmring4.html#E4:45"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">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="c9">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> 
<b>by </b><i><a class="txt" href="scmring4.html#E24:45_1"><i><font color="Green" title="E41">A10</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="txt" href="scmring4.html#E25:45_1"><i><font color="Green" title="E42">A11</font></i></a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a><br/>


</div><b>end;</b></div>
<a NAME="E30:45_1"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<b>hence </b><a NAME="E31:45_1"/>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">s2</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E23:45_1"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>

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

<a NAME="E32:45_1"/>
 <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E33:45_1"/><b>then </b><i><font color="Green" title="E43">A12</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/>
<a NAME="E34:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E35:45_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</a></i>;<br/>
<a NAME="E36:45_1"/><b>then </b><i><font color="Green" title="E44">A13</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E37:45_1"/><i><font color="Green" title="E45">A14</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E38:45_1"/><b>then </b><i><font color="Green" title="E46">A15</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E39:45_1"/><i><font color="Green" title="E47">A16</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E40:45_1"/><b>then </b><i><font color="Green" title="E48">A17</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E38:45_1"><i><font color="Green" title="E46">A15</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E41:45_1"/><i><font color="Green" title="E49">A18</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E42:45_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E40:45_1"><i><font color="Green" title="E48">A17</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E50">A19</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c13">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E21:45_1"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E40:45_1"><i><font color="Green" title="E48">A17</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E38:45_1"><i><font color="Green" title="E46">A15</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E44:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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="c9">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E45:45_1"/><b>then </b><i><font color="Green" title="E51">A20</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E46:45_1"/><i><font color="Green" title="E52">A21</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</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">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E47:45_1"/><i><font color="Green" title="E53">A22</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d2</font>
 
<b>by </b><i><a class="ref" href="scmring4.html#T20" target="_self" title="SCMRING4:th.20">Th20</a></i>;<br/>
<a NAME="E48:45_1"/><b>then </b><i><font color="Green" title="E54">A23</font></i>: 
not <font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E46:45_1"><i><font color="Green" title="E52">A21</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E49:45_1"/><i><font color="Green" title="E55">A24</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E50:45_1"/><b>then </b><i><font color="Green" title="E56">A25</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E45:45_1"><i><font color="Green" title="E51">A20</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E51:45_1"/><i><font color="Green" title="E57">A26</font></i>: 
<font color="Maroon" title="c9">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/>
<a NAME="E52:45_1"/><b>then </b><i><font color="Green" title="E58">A27</font></i>: 
not <font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E37:45_1"><i><font color="Green" title="E45">A14</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E53:45_1"/><i><font color="Green" title="E59">A28</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E39:45_1"><i><font color="Green" title="E47">A16</font></i></a>, <a class="txt" href="scmring4.html#E50:45_1"><i><font color="Green" title="E56">A25</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E54:45_1"/><b>then </b>
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E41:45_1"><i><font color="Green" title="E49">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E60">A29</font></i>: <font color="Maroon" title="c13">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c9">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E21:45_1"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E53:45_1"><i><font color="Green" title="E59">A28</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E52:45_1"><i><font color="Green" title="E58">A27</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E48:45_1"><i><font color="Green" title="E54">A23</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E56:45_1"/><i><font color="Green" title="E61">A30</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E46:45_1"><i><font color="Green" title="E52">A21</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E57:45_1"/><b>then </b><i><font color="Green" title="E62">A31</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E49:45_1"><i><font color="Green" title="E55">A24</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E58:45_1"/><i><font color="Green" title="E63">A32</font></i>: 
<font color="Maroon" title="c7">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T3" title="SCMRING3:th.3">SCMRING3:3</a></i>;<br/>
<a NAME="E59:45_1"/><b>then </b><i><font color="Green" title="E64">A33</font></i>: 
not <font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E37:45_1"><i><font color="Green" title="E45">A14</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E60:45_1"/><i><font color="Green" title="E65">A34</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E39:45_1"><i><font color="Green" title="E47">A16</font></i></a>, <a class="txt" href="scmring4.html#E57:45_1"><i><font color="Green" title="E62">A31</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E61:45_1"/><b>then </b>
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E41:45_1"><i><font color="Green" title="E49">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E66">A35</font></i>: <font color="Maroon" title="c13">s1</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p5">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E21:45_1"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p4">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E60:45_1"><i><font color="Green" title="E65">A34</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E59:45_1"><i><font color="Green" title="E64">A33</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E56:45_1"><i><font color="Green" title="E61">A30</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="txt" href="scmring4.html#E43:45_1"><i><font color="Green" title="E50">A19</font></i></a>, <a class="txt" href="scmring4.html#E55:45_1"><i><font color="Green" title="E60">A29</font></i></a>, <a class="txt" href="scmring4.html#E62:45_1"><i><font color="Green" title="E66">A35</font></i></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></i>
;<br/>
<a NAME="E64:45_1"/><b>then </b><i><font color="Green" title="E67">A36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="scmring4.html#E2:45_1"><i><font color="Green" title="E35">A4</font></i></a>, <a class="txt" href="scmring4.html#E33:45_1"><i><font color="Green" title="E43">A12</font></i></a>, <a class="txt" href="scmring4.html#E36:45_1"><i><font color="Green" title="E44">A13</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E65:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E66:45_1"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" title="AMI_1:th.80">AMI_1:80</a></i>;<br/>
<a NAME="E67:45_1"/><b>then </b><i><font color="Green" title="E68">A37</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E68:45_1"/><i><font color="Green" title="E69">A38</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E69:45_1"/><b>then </b><i><font color="Green" title="E70">A39</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E70:45_1"/><i><font color="Green" title="E71">A40</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</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#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E71:45_1"/><b>then </b><i><font color="Green" title="E72">A41</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E69:45_1"><i><font color="Green" title="E70">A39</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E72:45_1"/><i><font color="Green" title="E73">A42</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E73:45_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E71:45_1"><i><font color="Green" title="E72">A41</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E74">A43</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c14">s2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E23:45_1"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E71:45_1"><i><font color="Green" title="E72">A41</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmring4.html#E69:45_1"><i><font color="Green" title="E70">A39</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E75:45_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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="c9">il</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E76:45_1"/><b>then </b><i><font color="Green" title="E75">A44</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E77:45_1"/><i><font color="Green" title="E76">A45</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></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">d2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E78:45_1"/><b>then </b><i><font color="Green" title="E77">A46</font></i>: 
not <font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E47:45_1"><i><font color="Green" title="E53">A22</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E79:45_1"/><i><font color="Green" title="E78">A47</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">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#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E80:45_1"/><b>then </b><i><font color="Green" title="E79">A48</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E76:45_1"><i><font color="Green" title="E75">A44</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E81:45_1"/><i><font color="Green" title="E80">A49</font></i>: 
not <font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E51:45_1"><i><font color="Green" title="E57">A26</font></i></a>, <a class="txt" href="scmring4.html#E68:45_1"><i><font color="Green" title="E69">A38</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E82:45_1"/><i><font color="Green" title="E81">A50</font></i>: 
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E70:45_1"><i><font color="Green" title="E71">A40</font></i></a>, <a class="txt" href="scmring4.html#E80:45_1"><i><font color="Green" title="E79">A48</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E83:45_1"/><b>then </b>
<font color="Maroon" title="c9">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E72:45_1"><i><font color="Green" title="E73">A42</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E82">A51</font></i>: <font color="Maroon" title="c14">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c9">il</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E23:45_1"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E82:45_1"><i><font color="Green" title="E81">A50</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E81:45_1"><i><font color="Green" title="E80">A49</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">il</font>
<b>by </b><i><a class="txt" href="scmring4.html#E78:45_1"><i><font color="Green" title="E77">A46</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<a NAME="E85:45_1"/><i><font color="Green" title="E83">A52</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E77:45_1"><i><font color="Green" title="E76">A45</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E86:45_1"/><b>then </b><i><font color="Green" title="E84">A53</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E79:45_1"><i><font color="Green" title="E78">A47</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E87:45_1"/><i><font color="Green" title="E85">A54</font></i>: 
not <font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E58:45_1"><i><font color="Green" title="E63">A32</font></i></a>, <a class="txt" href="scmring4.html#E68:45_1"><i><font color="Green" title="E69">A38</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E88:45_1"/><i><font color="Green" title="E86">A55</font></i>: 
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E70:45_1"><i><font color="Green" title="E71">A40</font></i></a>, <a class="txt" href="scmring4.html#E86:45_1"><i><font color="Green" title="E84">A53</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E89:45_1"/><b>then </b>
<font color="Maroon" title="c7">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E72:45_1"><i><font color="Green" title="E73">A42</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E87">A56</font></i>: <font color="Maroon" title="c14">s2</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c7">d2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E23:45_1"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <font color="Maroon" title="c9">il</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E88:45_1"><i><font color="Green" title="E86">A55</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">il</font> <a href="ami_1.html#K28" title="AMI_1:func.28">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">d1</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c7">d2</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E87:45_1"><i><font color="Green" title="E85">A54</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">d2</font> <a href="scmring4.html#K2" title="SCMRING4:func.2">.--&gt;</a> <font color="Maroon" title="c10">e</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d2</font>
<b>by </b><i><a class="txt" href="scmring4.html#E85:45_1"><i><font color="Green" title="E83">A52</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c10">e</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c5">d1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<font color="Maroon" title="c10">e</font>
<b>by </b><i><a class="txt" href="scmring4.html#E74:45_1"><i><font color="Green" title="E74">A43</font></i></a>, <a class="txt" href="scmring4.html#E84:45_1"><i><font color="Green" title="E82">A51</font></i></a>, <a class="txt" href="scmring4.html#E90:45_1"><i><font color="Green" title="E87">A56</font></i></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></i>
;<br/>
<b>hence </b><a NAME="E92:45_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c13">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c14">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E2:45_1"><i><font color="Green" title="E35">A4</font></i></a>, <a class="txt" href="scmring4.html#E19:45_1"><i><font color="Green" title="E38">A7</font></i></a>, <a class="txt" href="scmring4.html#E33:45_1"><i><font color="Green" title="E43">A12</font></i></a>, <a class="txt" href="scmring4.html#E64:45_1"><i><font color="Green" title="E67">A36</font></i></a>, <a class="txt" href="scmring4.html#E67:45_1"><i><font color="Green" title="E68">A37</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:45"/>
contradiction
 ;<br/>


</div>
