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

<a NAME="E1:27_1_1"/><i><font color="Green">E29</font></i>: 
 <a href="lattice3.html#K3">LattPOSet</a> <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <span class="p2">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice3.html#D2">LATTICE3:def 2</a></i>;<br/>
<a NAME="E2:27_1_1"/><i><font color="Green">E32</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:27_1_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:27_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span>
 ;<br/>

<a NAME="E2:27_1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>
 
;<br/>
<a NAME="E3:27_1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:27_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="yellow_1.html#D2">YELLOW_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:27_1_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:27_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 ;<br/>

<a NAME="E2:27_1_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <span class="p2">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D2">YELLOW_1:def 2</a></i>;<br/>
<a NAME="E3:27_1_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:27_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:27_1_1_1"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="conlat_1.html#D1" target="_self">Def1</a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:27_1_1"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:27_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span>
 ;<br/>

<a NAME="E2:27_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font>
 
;<br/>
<a NAME="E3:27_1_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<a NAME="E4:27_1_1_2"/>
 <a href="lattice3.html#K3">LattPOSet</a> <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <span class="p2">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice3.html#D2">LATTICE3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:27_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="conlat_1.html#D1" target="_self">Def1</a>, <a class="ref" href="yellow_1.html#D2">YELLOW_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:27_1_1"/>
 <a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font> is   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


</div>
