
theorem
  for C being FormalContext for CP being FormalConcept of C holds (the
Extent of CP = {} implies CP is co-universal) & (the Intent of CP = {} implies
  CP is universal)
proof
  let C be FormalContext;
  let CP be FormalConcept of C;
A1: (AttributeDerivation(C)).(the Intent of CP) = the Extent of CP by Def9;
A2: the Intent of CP = {} implies CP is universal by A1,Th18;
A3: (ObjectDerivation(C)).(the Extent of CP) = the Intent of CP by Def9;
   the Extent of CP = {} implies CP is co-universal by A3,Th17;
  hence thesis by A2;
end;
