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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">CP</font> being  <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">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/><span class="kw">let </span><font color="Maroon" title="c2">CP</font> be   <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>



<span class="kw">consider </span><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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E2:85"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> <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#G2" title="CONLAT_1:aggr.2">ConceptStr</a>(# <font color="Maroon" title="c3">O</font>,<font color="Maroon" title="c4">A</font> #)
 <span class="kw">and </span><br/><a NAME="E3:85"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
<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#U2" title="CONLAT_1:sel.2">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#U2" title="CONLAT_1:sel.2">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>
 <span class="kw">and </span><br/><a NAME="E4:85"/><span class="lab"><font color="Green" title="E49">A3</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U3" title="CONLAT_1:sel.3">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#U3" title="CONLAT_1:sel.3">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#D22" target="_self" title="CONLAT_1:def.22">Def22</a></span>;<br/>
<span class="lab"><font color="Green" title="E50">A4</font></span>: <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#U2" title="CONLAT_1:sel.2">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></span>
<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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
<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#U2" title="CONLAT_1:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></span>
<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#U3" title="CONLAT_1:sel.3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></span>
<br/>.= 
the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></span>
;<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#U2" title="CONLAT_1:sel.2">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#U3" title="CONLAT_1:sel.3">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:85"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></span>
<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#U2" title="CONLAT_1:sel.2">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#U2" title="CONLAT_1:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></span>
<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#U2" title="CONLAT_1:sel.2">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#U2" title="CONLAT_1:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T16" target="_self" title="CONLAT_1:th.16">Th16</a></span>
<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#U2" title="CONLAT_1:sel.2">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></span>
<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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
<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#U2" title="CONLAT_1:sel.2">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#T24" target="_self" title="CONLAT_1:th.24">Th24</a></span>
<br/>.= 
the <a href="conlat_1.html#U3" title="CONLAT_1:sel.3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:85"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:85"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E5:85"><span class="lab"><font color="Green" title="E50">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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