
theorem
  for C being FormalContext for O being Subset of the carrier of C for A
  being Subset of the carrier' of C holds O c= (AttributeDerivation(C)).A iff A
  c= (ObjectDerivation(C)).O
proof
  let C be FormalContext;
  let O be Subset of the carrier of C;
  let A be Subset of the carrier' of C;
  O c= (AttributeDerivation(C)).A iff [:O,A:] c= the Information of C by Th9;
  hence thesis by Th10;
end;
