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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="conlat_1.html#NM1" title="CONLAT_1:NM.1">FormalContext</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">CP</font> being <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">CP</font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span><br/><b>let </b><font color="Maroon" title="c2">CP</font> be  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">CP</font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span><br/>



<b>consider </b><font color="Maroon" title="c3">O</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c4">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E2:82"/><i><font color="Green" title="E48">A1</font></i>: 
( <span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">CP</font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Maroon" title="c3">O</font>,<font color="Maroon" title="c4">A</font> #) &amp; <font color="Maroon" title="c3">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p3">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> )
 <b>by </b><i><a class="ref" href="conlat_1.html#D22" target="_self" title="CONLAT_1:def.22">Def22</a></i>;<br/>
<i><font color="Green" title="E49">A2</font></i>: <font color="Maroon" title="c3">O</font> = 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="conlat_1.html#E2:82"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p2">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
<br/>.= 
the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
;<br/>
<font color="Maroon" title="c4">A</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="txt" href="conlat_1.html#E2:82"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p2">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p2">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T16" target="_self" title="CONLAT_1:th.16">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></i>
<br/>.= 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
;<br/>
<b>hence </b><a NAME="E5:82"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">CP</font>,<span class="p1">(<span class="default"><a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#K5" title="CONLAT_1:func.5">Concept-with-all-Objects</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="conlat_1.html#E2:82"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="conlat_1.html#E3:82"><i><font color="Green" title="E49">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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