let C be FormalContext; :: thesis: for CP1, CP2 being strict FormalConcept of C holds (B-join C) . CP1,CP2 = (B-join C) . CP2,CP1
let CP1, CP2 be strict FormalConcept of C; :: thesis: (B-join C) . CP1,CP2 = (B-join C) . CP2,CP1
( ex O being Subset of the carrier of C ex A being Subset of the carrier' of C st
( (B-join C) . CP1,CP2 = ConceptStr(# O,A #) & O = (AttributeDerivation C) . ((ObjectDerivation C) . (the Extent of CP1 \/ the Extent of CP2)) & A = 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-join C) . CP2,CP1 = ConceptStr(# O9,A9 #) & O9 = (AttributeDerivation C) . ((ObjectDerivation C) . (the Extent of CP2 \/ the Extent of CP1)) & A9 = the Intent of CP2 /\ the Intent of CP1 ) ) by Def22;
hence (B-join C) . CP1,CP2 = (B-join C) . CP2,CP1 ; :: thesis: verum