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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>,  <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>,   <a href="hidden.html#M1">set</a> ] means 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" target="_self">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" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">a<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">a<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">a<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> );<br/>
<a NAME="E1:70_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<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="70_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> = the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</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#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E2:70_1_1_1"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</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#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</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#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="conlat_1.html#T8" target="_self">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">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" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">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" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T17" target="_self">Th17</a></i>
<br/>.= 
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">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" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>
;<br/>
<b>hence </b><a NAME="E2:70_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</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#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:70_1_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E4:70_1_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
not  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> #) is <a href="conlat_1.html#V7" target="_self">empty</a>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E2:70_1_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conlat_1.html#E32"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> #);<br/>
<a NAME="E5:70_1_1_1"/>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> #) <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3" target="_self">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" target="_self">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" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> : ( not  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) is <a href="conlat_1.html#V7" target="_self">empty</a> &amp; <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</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> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_1.html#E2:70_1_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conlat_1.html#E3:70_1_1_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conlat_1.html#E4:70_1_1_1"><i><font color="Green">E39</font></i></a></i>;<br/>
<a NAME="E6:70_1_1_1"/><b>then </b>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> #) <a href="hidden.html#R2">in</a>  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E7:70_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font>]
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:70_1_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3">BINOP_1:sch 3</a>(<a class="txt" href="conlat_1.html#E1:70_1_1"><i><font color="Green">E36</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="binop_1.html#NM2">BinOp</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E5:70_1_1"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</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#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>4</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> #) &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:70_1_1_2"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is    <a href="conlat_1.html#M2" target="_self">Element</a> of  <a href="conlat_1.html#K8" target="_self">B-carrier</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self">Th35</a></i>;<br/>
<b>thus </b><a NAME="E2:70_1_1_2"/>
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" target="_self">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" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> #) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:70_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conlat_1.html#E1:70_1_1_2"><i><font color="Green">E39</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E6:70_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="conlat_1.html#V6" target="_self">strict</a> <a href="conlat_1.html#NM4">FormalConcept</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#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>4</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> #) &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">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" target="_self">AttributeDerivation</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E5:70_1_1"><i><font color="Green">E38</font></i></a></i>;<br/>


</div>
