<?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>let </b><font color="Maroon">CP</font> be  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>;<br/>



<b>set </b><font color="Maroon">D</font> = <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 <font color="Maroon">CP</font> &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/>
<a NAME="E1:12"/><i><font color="Green">E22</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 <font color="Maroon">CP</font> &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="lattice3.html#R4">is_less_than</a>  <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">q</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="lattice3.html#D17">LATTICE3:def 17</a><br/>

<b>assume </b><a NAME="E1:12_1"/>
<font color="Maroon">q</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 <font color="Maroon">CP</font> &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="E3:12_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">q</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 <font color="Maroon">CP</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="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="E5:12_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">CP</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/>;<br/>
<a NAME="E6:12_1"/><i><font color="Green">E26</font></i>: 
<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> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">CP</font>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E7:12_1"/><i><font color="Green">E27</font></i>: 
<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> the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">CP</font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5">Intent</a> of <font color="Maroon">CP</font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D13">CONLAT_1:def 13</a></i>;<br/>
<a NAME="E8:12_1"/>
the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="conlat_1.html#K12">@</a> </span>)</span> <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>, , <a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>
<a NAME="E9:12_1"/><b>then </b>
the <a href="conlat_1.html#U5">Intent</a> of <font color="Maroon">CP</font> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<b>by </b><i>, , <a class="ref" href="conlat_1.html#T3">CONLAT_1:3</a></i>;<br/>
<a NAME="E10:12_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">q</font> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">CP</font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T31">CONLAT_1:31</a></i>;<br/>
<a NAME="E11:12_1"/>
<font color="Maroon">CP</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font></span>)</span> <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="E12:12_1"/>
<font color="Maroon">q</font> <a href="lattices.html#R1">[=</a>  <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font>
 <b>by </b><i>, <a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:12"/>
for <font color="Olive">CP'</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>  st <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 <font color="Maroon">CP</font> &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="lattice3.html#R4">is_less_than</a> <font color="Olive">CP'</font> holds <br/> <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font> <a href="lattices.html#R3">[=</a> <font color="Olive">CP'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">CP'</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>;<br/>

<b>assume </b><a NAME="E1:12_2"/><i><font color="Green">E41</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 <font color="Maroon">CP</font> &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="lattice3.html#R4">is_less_than</a> <font color="Maroon">CP'</font>
 ;<br/>

<a NAME="E2:12_2"/><i><font color="Green">E43</font></i>: 
the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">CP</font> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">CP'</font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_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="E1:12_2_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">CP</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">C</font> ;<br/>
<b>set </b><font color="Maroon">Ox</font> = <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">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon">Ax</font> = <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">x</font></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon">Cx</font> =  <a href="conlat_1.html#G3">ConceptStr</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">(<span class="default"><span class="p3">(<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="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>,<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">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> #) as  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T20">CONLAT_1:20</a></i>;<br/>
<a NAME="E4:12_2_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</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">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T5">CONLAT_1:5</a></i>;<br/>
<a NAME="E5:12_2_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">Cx</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E6:12_2_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">Cx</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 <font color="Maroon">CP</font> &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> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:12_2_1"/>
 <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">Cx</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">CP'</font>
 
<b>by </b><i>, , <a class="ref" href="lattice3.html#D17">LATTICE3:def 17</a></i>;<br/>
<a NAME="E8:12_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">Cx</font></span>)</span> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">CP'</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>
<a NAME="E9:12_2_1"/>
<font color="Maroon">Cx</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">Cx</font></span>)</span> <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/>
<a NAME="E10:12_2_1"/><b>then </b>
the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">Cx</font> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">CP'</font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="conlat_1.html#D19">CONLAT_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E11:12_2_1"/>
<font color="Maroon">x</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">CP'</font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E3:12_2"/>
<font color="Maroon">CP</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font></span>)</span> <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/>
<a NAME="E4:12_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font></span>)</span> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">CP'</font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i>, <a class="ref" href="conlat_1.html#D19">CONLAT_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E5:12_2"/>
 <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">CP'</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:12"/><b>then </b>
 <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 <font color="Maroon">CP</font> &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>  <a href="conlat_2.html#K1" target="_self">@</a> <font color="Maroon">CP</font>
 
<b>by </b><i>, <a class="ref" href="lattice3.html#D21">LATTICE3:def 21</a></i>;<br/>
<b>hence </b><a NAME="E4:12"/>
 <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 <font color="Maroon">CP</font> &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">CP</font>
 ;<br/>


</div>
