let C be FormalContext; :: thesis: for CP1, CP2 being strict FormalConcept of C holds (B-meet C) . (CP1,CP2) = (B-meet C) . (CP2,CP1)
let CP1, CP2 be strict FormalConcept of C; :: thesis: (B-meet C) . (CP1,CP2) = (B-meet C) . (CP2,CP1)
( ex O being Subset of the carrier of C ex A being Subset of the carrier' of C st
( (B-meet C) . (CP1,CP2) = ConceptStr(# O,A #) & O = the Extent of CP1 /\ the Extent of CP2 & A = (ObjectDerivation C) . ((AttributeDerivation C) . ( the Intent of CP1 \/ the Intent of CP2)) ) & ex O9 being Subset of the carrier of C ex A9 being Subset of the carrier' of C st
( (B-meet C) . (CP2,CP1) = ConceptStr(# O9,A9 #) & O9 = the Extent of CP2 /\ the Extent of CP1 & A9 = (ObjectDerivation C) . ((AttributeDerivation C) . ( the Intent of CP2 \/ the Intent of CP1)) ) ) by Def17;
hence (B-meet C) . (CP1,CP2) = (B-meet C) . (CP2,CP1) ; :: thesis: verum