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

<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> holds <br/> ( the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">D</font> </span>}</span> </span>)</span></span>)</span> &amp; the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">D</font> </span>}</span>  )</span><br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span> &amp; the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )</span><br/>



<b>set </b><font color="Maroon" title="c3">O</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span>;<br/>
<a NAME="E1:10"/><i><font color="Green" title="E5">A1</font></i>: 
 <a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="conlat_1.html#D23" title="CONLAT_1:def.23">CONLAT_1:def 23</a></i>;<br/>
<a NAME="E2:10"/><i><font color="Green" title="E6">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> holds <br/>( <font color="Olive" title="b1">x</font> is  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> &amp;  ex <font color="Olive" title="b2">E</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b3">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> implies ( <font color="Maroon" title="c4">x</font> is  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> &amp;  ex <font color="Olive" title="b1">E</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) ) )</span><br/>

<b>assume </b><a NAME="E1:10_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> is  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> &amp;  ex <font color="Olive" title="b1">E</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) )</span><br/>

<a NAME="E2:10_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> is  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:10"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="conlat_1.html#T35" title="CONLAT_1:th.35">CONLAT_1:35</a></i>;<br/>
<b>hence </b><a NAME="E3:10_1"/>
( <font color="Maroon" title="c4">x</font> is  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> &amp;  ex <font color="Olive" title="b1">E</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:10"/>
<span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<b>assume </b><a NAME="E1:10_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c6">I</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:10_2"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c6">I</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c6">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 ;<br/>
<b>thus </b><a NAME="E4:10_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_2"><i><font color="Green" title="E7">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c4">OO</font> = <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<b>set </b><font color="Maroon" title="c5">A'</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c6">y</font> being    <a href="conlat_1.html#M3" title="CONLAT_1:mode.3">Element</a> of <font color="Maroon" title="c2">D</font>;<br/>
<b>consider </b><font color="Maroon" title="c7">E'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c8">I'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E7:10"/><i><font color="Green" title="E7">A4</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c7">E'</font>,<font color="Maroon" title="c8">I'</font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<a NAME="E8:10"/>
the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E7:10"><i><font color="Green" title="E7">A4</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">OO</font> = <font color="Maroon" title="c4">OO</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E10:10"/><i><font color="Green" title="E8">A5</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">OO</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_2.html#T2" target="_self" title="CONLAT_2:th.2">Th2</a></i>;<br/>
<a NAME="E11:10"/><i><font color="Green" title="E9">A6</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:10_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span>  or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:10_3_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c11">O'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:10_3_1"/><i><font color="Green" title="E10">A7</font></i>: 
( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">O'</font> &amp; <font color="Maroon" title="c11">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )
 ;<br/>
<b>consider </b><font color="Maroon" title="c12">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c13">I</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E5:10_3_1"/><i><font color="Green" title="E11">A8</font></i>: 
( <font color="Maroon" title="c11">O'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c12">E</font>,<font color="Maroon" title="c13">I</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c12">E</font>,<font color="Maroon" title="c13">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_3_1"><i><font color="Green" title="E10">A7</font></i></a></i>;<br/>
<a NAME="E6:10_3_1"/>
 <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c12">E</font>,<font color="Maroon" title="c13">I</font> #) is   <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="conlat_2.html#E5:10_3_1"><i><font color="Green" title="E11">A8</font></i></a></i>;<br/>
<a NAME="E7:10_3_1"/><b>then </b>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c12">E</font>,<font color="Maroon" title="c13">I</font> #)
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:10_3_1"><i><font color="Green" title="E10">A7</font></i></a>, <a class="txt" href="conlat_2.html#E5:10_3_1"><i><font color="Green" title="E11">A8</font></i></a>, <a class="ref" href="conlat_1.html#D13" title="CONLAT_1:def.13">CONLAT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E8:10_3_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:10_3_1"><i><font color="Green" title="E11">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>thus </b><a NAME="E2:10_3"/>
<span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:10_3_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c11">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c12">I</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:10_3_2"/><i><font color="Green" title="E10">A9</font></i>: 
( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">E</font>,<font color="Maroon" title="c12">I</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">E</font>,<font color="Maroon" title="c12">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 ;<br/>
<a NAME="E4:10_3_2"/>
 <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">E</font>,<font color="Maroon" title="c12">I</font> #) is   <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="conlat_2.html#E3:10_3_2"><i><font color="Green" title="E10">A9</font></i></a></i>;<br/>
<a NAME="E5:10_3_2"/><b>then </b><i><font color="Green" title="E11">A10</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">E</font>,<font color="Maroon" title="c12">I</font> #)
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:10_3_2"><i><font color="Green" title="E10">A9</font></i></a>, <a class="ref" href="conlat_1.html#D13" title="CONLAT_1:def.13">CONLAT_1:def 13</a></i>;<br/>
<a NAME="E6:10_3_2"/>
the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">E</font>,<font color="Maroon" title="c12">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">EE</font>,<font color="Olive" title="b2">II</font> #) where <font color="Olive" title="b1">EE</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">II</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">EE</font>,<font color="Olive" title="b2">II</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:10_3_2"><i><font color="Green" title="E10">A9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:10_3_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">O'</font></span>)</span> where <font color="Olive" title="b1">O'</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">O'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:10_3_2"><i><font color="Green" title="E11">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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


</div><b>end;</b></div>
<a NAME="E12:10"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span> or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<b>assume </b><a NAME="E1:10_4"/><i><font color="Green" title="E10">A11</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font></span><br/>

<b>consider </b><font color="Maroon" title="c11">Y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> ;<br/>
<b>consider </b><font color="Maroon" title="c12">y</font> being    <a href="conlat_1.html#M3" title="CONLAT_1:mode.3">Element</a> of <font color="Maroon" title="c2">D</font>;<br/>
<b>consider </b><font color="Maroon" title="c13">E'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c14">I'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E5:10_4"/><i><font color="Green" title="E11">A12</font></i>: 
<font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c13">E'</font>,<font color="Maroon" title="c14">I'</font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<a NAME="E6:10_4"/><i><font color="Green" title="E12">A13</font></i>: 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E5:10_4"><i><font color="Green" title="E11">A12</font></i></a></i>;<br/>
<a NAME="E7:10_4"/><b>then </b>
<font color="Maroon" title="c11">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c15">E1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c16">I1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E9:10_4"/><i><font color="Green" title="E13">A14</font></i>: 
( <font color="Maroon" title="c11">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c15">E1</font>,<font color="Maroon" title="c16">I1</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c15">E1</font>,<font color="Maroon" title="c16">I1</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 ;<br/>
<a NAME="E10:10_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">Y</font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E10:10"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="conlat_2.html#E11:10"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="conlat_2.html#E1:10_4"><i><font color="Green" title="E10">A11</font></i></a>, <a class="txt" href="conlat_2.html#E6:10_4"><i><font color="Green" title="E12">A13</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:10_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E9:10_4"><i><font color="Green" title="E13">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c10">a</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E14:10"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span> or <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<b>assume </b><a NAME="E1:10_5"/><i><font color="Green" title="E10">A15</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span><br/>

<b>set </b><font color="Maroon" title="c12">u</font> =  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> ;<br/>
<a NAME="E2:10_5"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  or <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<b>assume </b><a NAME="E1:10_5_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span><br/>

<b>then consider </b><font color="Maroon" title="c14">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:10_5_1"/><i><font color="Green" title="E11">A16</font></i>: 
( <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c14">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c16">I</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E5:10_5_1"/><i><font color="Green" title="E12">A17</font></i>: 
( <font color="Maroon" title="c14">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c15">E</font>,<font color="Maroon" title="c16">I</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c15">E</font>,<font color="Maroon" title="c16">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_5_1"><i><font color="Green" title="E11">A16</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:10_5_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_5_1"><i><font color="Green" title="E11">A16</font></i></a>, <a class="txt" href="conlat_2.html#E5:10_5_1"><i><font color="Green" title="E12">A17</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c13">u</font> =  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E4:10_5"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">u</font></span>)</span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
;<br/>
<b>hence </b><a NAME="E5:10_5"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E1:10_5"><i><font color="Green" title="E10">A15</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c11">o</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E16:10"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  or <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<b>assume </b><a NAME="E1:10_6"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span><br/>

<b>then consider </b><font color="Maroon" title="c13">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:10_6"/><i><font color="Green" title="E10">A18</font></i>: 
( <font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c13">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">E</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c15">I</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E5:10_6"/><i><font color="Green" title="E11">A19</font></i>: 
( <font color="Maroon" title="c13">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c14">E</font>,<font color="Maroon" title="c15">I</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c14">E</font>,<font color="Maroon" title="c15">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_6"><i><font color="Green" title="E10">A18</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:10_6"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_6"><i><font color="Green" title="E10">A18</font></i></a>, <a class="txt" href="conlat_2.html#E5:10_6"><i><font color="Green" title="E11">A19</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c12">CP'</font> =  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c10">a</font> #) as  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="ref" href="conlat_1.html#T20" title="CONLAT_1:th.20">CONLAT_1:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">CP</font> = <font color="Maroon" title="c12">CP'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E1:10"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="conlat_1.html#T35" title="CONLAT_1:th.35">CONLAT_1:35</a></i>;<br/>
<a NAME="E19:10"/><i><font color="Green" title="E10">A20</font></i>: 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c13">CP</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E10:10"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="conlat_2.html#E11:10"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="conlat_1.html#D24" title="CONLAT_1:def.24">CONLAT_1:def 24</a></i>;<br/>
<a NAME="E20:10"/><i><font color="Green" title="E11">A21</font></i>: 
<font color="Maroon" title="c2">D</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Maroon" title="c13">CP</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17" title="LATTICE3:def.17">LATTICE3:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c14">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> or <font color="Maroon" title="c14">q</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c13">CP</font> )</span><br/>

<b>assume </b><a NAME="E1:10_7"/>
<font color="Maroon" title="c14">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c14">q</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c13">CP</font></span><br/>

<a NAME="E2:10_7"/><b>then </b>
<font color="Maroon" title="c14">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D24" title="CONLAT_1:def.24">CONLAT_1:def 24</a></i>;<br/>
<a NAME="E3:10_7"/><b>then </b>
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
;<br/>
<a NAME="E4:10_7"/><b>then </b>
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c13">CP</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E19:10"><i><font color="Green" title="E10">A20</font></i></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>;<br/>
<a NAME="E5:10_7"/><b>then </b>
<font color="Maroon" title="c14">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a>  <a href="conlat_1.html#R2" title="CONLAT_1:pred.2">is-SubConcept-of</a> <font color="Maroon" title="c13">CP</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#T31" title="CONLAT_1:th.31">CONLAT_1:31</a></i>;<br/>
<b>hence </b><a NAME="E6:10_7"/>
<font color="Maroon" title="c14">q</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c13">CP</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47" title="CONLAT_1:th.47">CONLAT_1:47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E21:10"/>
for <font color="Olive" title="b1">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>  st <font color="Maroon" title="c2">D</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Olive" title="b1">r</font> holds <br/><font color="Maroon" title="c13">CP</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b1">r</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">D</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Maroon" title="c14">r</font> implies <font color="Maroon" title="c13">CP</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c14">r</font> )</span><br/>

<b>assume </b><a NAME="E1:10_8"/><i><font color="Green" title="E12">A22</font></i>: 
<font color="Maroon" title="c2">D</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Maroon" title="c14">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c13">CP</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c14">r</font></span><br/>

<a NAME="E2:10_8"/><i><font color="Green" title="E13">A23</font></i>: 
for <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>  st <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> holds <br/>the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c15">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> implies the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c15">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:10_8_1"/>
<font color="Maroon" title="c15">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c15">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span></span><br/>

<a NAME="E2:10_8_1"/><b>then </b>
<font color="Maroon" title="c15">q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c14">r</font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:10_8"><i><font color="Green" title="E12">A22</font></i></a>, <a class="ref" href="lattice3.html#D17" title="LATTICE3:def.17">LATTICE3:def 17</a></i>;<br/>
<a NAME="E3:10_8_1"/><b>then </b>
<font color="Maroon" title="c15">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a>  <a href="conlat_1.html#R2" title="CONLAT_1:pred.2">is-SubConcept-of</a> <font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#T47" title="CONLAT_1:th.47">CONLAT_1:47</a></i>;<br/>
<b>hence </b><a NAME="E4:10_8_1"/>
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c15">q</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 <b>by </b><i><a class="ref" href="conlat_1.html#T31" title="CONLAT_1:th.31">CONLAT_1:31</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:10_8"/>
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_8_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c15">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> or <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:10_8_2"/><i><font color="Green" title="E14">A24</font></i>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span><br/>

<b>consider </b><font color="Maroon" title="c16">y</font> being    <a href="conlat_1.html#M3" title="CONLAT_1:mode.3">Element</a> of <font color="Maroon" title="c2">D</font>;<br/>
<b>consider </b><font color="Maroon" title="c17">E'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c18">I'</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E4:10_8_2"/><i><font color="Green" title="E15">A25</font></i>: 
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c17">E'</font>,<font color="Maroon" title="c18">I'</font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:10"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<a NAME="E5:10_8_2"/><i><font color="Green" title="E16">A26</font></i>: 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E4:10_8_2"><i><font color="Green" title="E15">A25</font></i></a></i>;<br/>
<a NAME="E6:10_8_2"/>
for <font color="Olive" title="b1">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) where <font color="Olive" title="b2">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b3">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  holds <br/><font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_8_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c19">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  implies <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">Y</font> )</span><br/>

<b>assume </b><a NAME="E1:10_8_2_1"/>
<font color="Maroon" title="c19">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">Y</font></span><br/>

<b>then consider </b><font color="Maroon" title="c20">Ey</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c21">Iy</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:10_8_2_1"/><i><font color="Green" title="E17">A27</font></i>: 
( <font color="Maroon" title="c19">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c20">Ey</font>,<font color="Maroon" title="c21">Iy</font> #) &amp;  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c20">Ey</font>,<font color="Maroon" title="c21">Iy</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c22">C1</font> =  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c20">Ey</font>,<font color="Maroon" title="c21">Iy</font> #) as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_8_2_1"><i><font color="Green" title="E17">A27</font></i></a></i>;<br/>
<a NAME="E5:10_8_2_1"/>
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c22">C1</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:10_8"><i><font color="Green" title="E13">A23</font></i></a>, <a class="txt" href="conlat_2.html#E3:10_8_2_1"><i><font color="Green" title="E17">A27</font></i></a></i>;<br/>
<a NAME="E6:10_8_2_1"/><b>then </b>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c22">C1</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:10_8_2"><i><font color="Green" title="E14">A24</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:10_8_2_1"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">Y</font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:10_8_2_1"><i><font color="Green" title="E17">A27</font></i></a>, <a class="ref" href="conlat_1.html#D24" title="CONLAT_1:def.24">CONLAT_1:def 24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:10_8_2"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:10_8_2"><i><font color="Green" title="E16">A26</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:10_8"/><b>then </b>
<font color="Maroon" title="c13">CP</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a>  <a href="conlat_1.html#R2" title="CONLAT_1:pred.2">is-SubConcept-of</a> <font color="Maroon" title="c14">r</font> <a href="conlat_1.html#K12" title="CONLAT_1:func.12">@</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E19:10"><i><font color="Green" title="E10">A20</font></i></a>, <a class="ref" href="conlat_1.html#T31" title="CONLAT_1:th.31">CONLAT_1:31</a></i>;<br/>
<b>hence </b><a NAME="E5:10_8"/>
<font color="Maroon" title="c13">CP</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c14">r</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47" title="CONLAT_1:th.47">CONLAT_1:47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E22:10"/>
( the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span> </span>)</span></span>)</span> &amp; the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K3" title="CONLAT_2:func.3">"\/"</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> :  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font> </span>}</span>  )
 <b>by </b><i><a class="txt" href="conlat_2.html#E10:10"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="conlat_2.html#E11:10"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="conlat_2.html#E20:10"><i><font color="Green" title="E11">A21</font></i></a>, <a class="ref" href="lattice3.html#D21" title="LATTICE3:def.21">LATTICE3:def 21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
