
theorem Th23:
  for C being FormalContext holds the Extent of
  Concept-with-all-Objects(C) = the carrier of C & the Intent of
  Concept-with-all-Attributes(C) = the carrier' of C
proof
  let C be FormalContext;
  (ex O being Subset of the carrier of C, A being Subset of the carrier'
  of C st Concept-with-all-Objects(C) = ConceptStr(#O,A#) & O = (
AttributeDerivation(C) ).({}) & A = (ObjectDerivation(C)).((AttributeDerivation
  (C)).({})) )& ex O being Subset of the carrier of C, A being Subset of the
  carrier' of C st Concept-with-all-Attributes(C) = ConceptStr(#O,A#) & O = (
AttributeDerivation( C)).((ObjectDerivation(C)).({})) & A = ( ObjectDerivation(
  C)).({}) by Def12,Def13;
  hence thesis by Th17,Th18;
end;
