
theorem Th33:
  for C being FormalContext for CP1,CP2 being strict FormalConcept
  of C holds (B-join(C)).(CP1,CP2) = (B-join(C)).(CP2,CP1)
proof
  let C be FormalContext;
  let CP1,CP2 be strict FormalConcept of C;
  (ex O being Subset of the carrier of C, 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, 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 Def18;
  hence thesis;
end;
