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

<b>let </b><font color="Maroon">C</font> be   <a href="conlat_1.html#NM1">FormalContext</a>;<br/>

<b>set </b><font color="Maroon">G</font> =  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span>;<br/>
<b>thus </b><a NAME="E1:17"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span> is <a href="lattice6.html#V8">supremum-dense</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice6.html#D13">LATTICE6:def 13</a><br/>

<a NAME="E1:17_1"/><i><font color="Green">E22</font></i>: 
 <a href="lattice3.html#K15">"\/"</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span> ) </span>}</span> ,<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:17_1"/><i><font color="Green">E23</font></i>: 
<span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_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> ; <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="E1:17_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">O</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Maroon">A</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:17_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">A</font> #) &amp;  ex <font color="Olive">o</font> being  <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">o</font></span><a href="domain_1.html#K6">}</a></span> ) )
 ;<br/>
<b>consider </b><font color="Maroon">o</font> being   <a href="conlat_1.html#NM2">Object</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E5:17_1_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i/>;<br/>
<a NAME="E6:17_1_1"/><i><font color="Green">E27</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span><b> such that </b><br/><a NAME="E8:17_1_1"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>
<b>consider </b><font color="Maroon">O'</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Maroon">A'</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E10:17_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">O'</font>,<font color="Maroon">A'</font> #) &amp; <font color="Maroon">O'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Maroon">A'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E11:17_1_1"/>
<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_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, , , , , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>
<b>hence </b><a NAME="E4:17_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><a href="conlat_2.html#K4" target="_self">gamma</a> <font color="Maroon">C</font></span>)</span></span>)</span> st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K15">"\/"</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<b>set </b><font color="Maroon">G</font> =  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice6.html#D14">LATTICE6:def 14</a><br/>

<a NAME="E2:17"/><i><font color="Green">E43</font></i>: 
 <a href="lattice3.html#K16">"/\"</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> ) </span>}</span> ,<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:17"/><i><font color="Green">E44</font></i>: 
<span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_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="E1:17_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">O</font>,<font color="Olive">A</font> #) where <font color="Olive">O</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font> :  ex <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Olive">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">O</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Maroon">A</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:17_2"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">O</font>,<font color="Maroon">A</font> #) &amp;  ex <font color="Olive">a</font> being  <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> ) )
 ;<br/>
<b>consider </b><font color="Maroon">a</font> being   <a href="conlat_1.html#NM3">Attribute</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E5:17_2"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> </span>)</span> &amp; <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> )
 <b>by </b><i/>;<br/>
<a NAME="E6:17_2"/><i><font color="Green">E49</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span><b> such that </b><br/><a NAME="E8:17_2"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>
<b>consider </b><font color="Maroon">O'</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <font color="Maroon">A'</font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E10:17_2"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">O'</font>,<font color="Maroon">A'</font> #) &amp; <font color="Maroon">O'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">A'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E11:17_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_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, , , , , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><a href="conlat_2.html#K5" target="_self">delta</a> <font color="Maroon">C</font></span>)</span></span>)</span> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K16">"/\"</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div>
