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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="conlat_1.html#NM1">FormalContext</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span></span>)</span>;<br/>
<a NAME="E1:11"/><i><font color="Green">E5</font></i>: 
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8">B-carrier</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9">B-meet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="conlat_1.html#D23">CONLAT_1:def 23</a></i>;<br/>
<a NAME="E2:11"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ex <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:11"><i><font color="Green">E5</font></i></a>, <a class="ref" href="conlat_1.html#T35">CONLAT_1:35</a></i>;<br/>
<b>hence </b><a NAME="E3:11_1"/>
( <font color="Maroon">c<sub>4</sub></font> is  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:11"/>
<span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:11_2"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>
<b>thus </b><a NAME="E4:11_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_2"><i><font color="Green">E7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  as   <a href="setfam_1.html#NM1">Subset-Family</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="conlat_1.html#M3">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:11"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:11"><i><font color="Green">E6</font></i></a></i>;<br/>
<a NAME="E8:11"/>
the <a href="conlat_1.html#U5">Intent</a> of <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E7:11"><i><font color="Green">E7</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E10:11"/><i><font color="Green">E8</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">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#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="conlat_2.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E11:11"/><i><font color="Green">E9</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#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:11_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_3_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">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#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:11_3_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:11_3_1"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_3_1"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E6:11_3_1"/>
 <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:11"><i><font color="Green">E6</font></i></a>, <a class="txt" href="conlat_2.html#E5:11_3_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E7:11_3_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> #)
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:11_3_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conlat_2.html#E5:11_3_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="conlat_1.html#D13">CONLAT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:11_3_1"><i><font color="Green">E11</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:11_3"/>
<span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  <a href="tarski.html#R1">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#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_3_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:11_3_2"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>
<a NAME="E4:11_3_2"/>
 <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:11"><i><font color="Green">E6</font></i></a>, <a class="txt" href="conlat_2.html#E3:11_3_2"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E5:11_3_2"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> #)
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:11_3_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="conlat_1.html#D13">CONLAT_1:def 13</a></i>;<br/>
<a NAME="E6:11_3_2"/>
the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> #) <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E3:11_3_2"><i><font color="Green">E10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:11_3_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">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#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:11_3_2"><i><font color="Green">E11</font></i></a></i>;<br/>


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


</div><b>end;</b></div>
<a NAME="E12:11"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_4"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="conlat_1.html#M3">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>14</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:11_4"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:11"><i><font color="Green">E6</font></i></a></i>;<br/>
<a NAME="E6:11_4"/><i><font color="Green">E12</font></i>: 
the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E5:11_4"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E7:11_4"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>16</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:11_4"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>
<a NAME="E10:11_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E10:11"><i><font color="Green">E8</font></i></a>, <a class="txt" href="conlat_2.html#E11:11"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conlat_2.html#E1:11_4"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conlat_2.html#E6:11_4"><i><font color="Green">E12</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:11_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E9:11_4"><i><font color="Green">E13</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E14:11"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_5"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> ;<br/>
<a NAME="E2:11_5"/>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_5_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:11_5_1"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>16</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:11_5_1"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_5_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:11_5_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_5_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conlat_2.html#E5:11_5_1"><i><font color="Green">E12</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> =  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E4:11_5"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E5:11_5"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E1:11_5"><i><font color="Green">E10</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E16:11"/>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_6"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:11_6"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:11_6"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_6"><i><font color="Green">E10</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:11_6"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_6"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conlat_2.html#E5:11_6"><i><font color="Green">E11</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> =  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> #) as  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="conlat_1.html#T22">CONLAT_1:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>12</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E1:11"><i><font color="Green">E5</font></i></a>, <a class="ref" href="conlat_1.html#T35">CONLAT_1:35</a></i>;<br/>
<a NAME="E19:11"/><i><font color="Green">E10</font></i>: 
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E10:11"><i><font color="Green">E8</font></i></a>, <a class="txt" href="conlat_2.html#E11:11"><i><font color="Green">E9</font></i></a>, <a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>
<a NAME="E20:11"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a><br/>

<b>assume </b><a NAME="E1:11_7"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:11_7"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>
<a NAME="E3:11_7"/><b>then </b>
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
;<br/>
<a NAME="E4:11_7"/><b>then </b>
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E19:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>;<br/>
<a NAME="E5:11_7"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#D19">CONLAT_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E6:11_7"/>
<font color="Maroon">c<sub>13</sub></font> <a href="lattices.html#R1">[=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:11"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:11_8"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="lattice3.html#R3">is_less_than</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:11_8"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/>the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:11_8_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:11_8_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:11_8"><i><font color="Green">E12</font></i></a>, <a class="ref" href="lattice3.html#D16">LATTICE3:def 16</a></i>;<br/>
<a NAME="E3:11_8_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">c<sub>15</sub></font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>
<b>hence </b><a NAME="E4:11_8_1"/>
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 <b>by </b><i><a class="ref" href="conlat_1.html#D19">CONLAT_1:def 19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:11_8"/>
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_8_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:11_8_2"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>16</sub></font> being    <a href="conlat_1.html#M3">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>18</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:11_8_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> #)
 <b>by </b><i><a class="txt" href="conlat_2.html#E2:11"><i><font color="Green">E6</font></i></a></i>;<br/>
<a NAME="E5:11_8_2"/><i><font color="Green">E16</font></i>: 
the <a href="conlat_1.html#U4">Extent</a> of <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E4:11_8_2"><i><font color="Green">E15</font></i></a></i>;<br/>
<a NAME="E6:11_8_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  holds <br/><font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_8_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:11_8_2_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>20</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>21</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:11_8_2_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font> #) &amp;  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>22</sub></font> =  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font> #) as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_8_2_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E5:11_8_2_1"/>
the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E2:11_8"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conlat_2.html#E3:11_8_2_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E6:11_8_2_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>22</sub></font> <a href="conlat_1.html#K12">@</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E1:11_8_2"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:11_8_2_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="conlat_2.html#E3:11_8_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="conlat_1.html#D24">CONLAT_1:def 24</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:11_8_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="conlat_2.html#E5:11_8_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:11_8"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="conlat_1.html#K12">@</a>  <a href="conlat_1.html#R2">is-SubConcept-of</a> <font color="Maroon">c<sub>13</sub></font> <a href="conlat_1.html#K12">@</a> 
 
<b>by </b><i><a class="txt" href="conlat_2.html#E19:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="conlat_1.html#D19">CONLAT_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E5:11_8"/>
<font color="Maroon">c<sub>14</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="conlat_1.html#T47">CONLAT_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:11"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattice3.html#K16">"/\"</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="conlat_2.html#E20:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="lattice3.html#T34">LATTICE3:34</a></i>;<br/>
<b>hence </b><a NAME="E23:11"/>
( the <a href="conlat_1.html#U4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> the <a href="conlat_1.html#U4">Extent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  &amp; the <a href="conlat_1.html#U5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_2.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> the <a href="conlat_1.html#U5">Intent</a> of <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) where B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> :  <a href="conlat_1.html#G3">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> </span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="conlat_2.html#E10:11"><i><font color="Green">E8</font></i></a>, <a class="txt" href="conlat_2.html#E11:11"><i><font color="Green">E9</font></i></a></i>;<br/>


</div>
