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<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  <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/>



<b>consider </b><font color="Maroon">c<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>, <font color="Maroon">c<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><b> such that </b><br/><a NAME="E2:83"/><i><font color="Green">E48</font></i>: 
( <span class="p1">(<span class="default"><a href="conlat_1.html#K10" target="_self">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K6" target="_self">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <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">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#K4">\/</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <span class="p3">(<span class="default"><a href="conlat_1.html#K6" target="_self">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 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#K9">/\</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K6" target="_self">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="conlat_1.html#D22" target="_self">Def22</a></i>;<br/>
<i><font color="Green">E49</font></i>: <font color="Maroon">c<sub>4</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#K8">/\</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="conlat_1.html#E2:83"><i><font color="Green">E48</font></i></a>, <a class="ref" href="conlat_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E4:83"/>
the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</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="E6:83"/>
<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>5</sub></font> <a href="tarski.html#R1">c=</a> <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> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E7:83"/><b>then </b><i><font color="Green">E50</font></i>: 
<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#K4">\/</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> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <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> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/>
<font color="Maroon">c<sub>3</sub></font> = 
<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">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#K4">\/</a> <span class="p3">(<span class="default"><span class="p4">(<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 <span class="p4">(<span class="default"><a href="conlat_1.html#K6" target="_self">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="conlat_1.html#E2:83"><i><font color="Green">E48</font></i></a>, <a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<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_1.html#K1">.</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_1.html#K1">.</a> <span class="p2">(<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="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<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_1.html#K1">.</a> the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
<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> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="conlat_1.html#E7:83"><i><font color="Green">E50</font></i></a>, <a class="ref" href="conlat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<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> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="conlat_1.html#T8" target="_self">Th8</a></i>
<br/>.= 
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">c<sub>2</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="E9:83"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" target="_self">B-join</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K6" target="_self">Concept-with-all-Attributes</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E2:83"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conlat_1.html#E3:83"><i><font color="Green">E49</font></i></a></i>;<br/>


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