
theorem
  for C being FormalContext for CP being quasi-empty ConceptStr over C
  st CP is FormalConcept of C holds CP is universal or CP is co-universal
proof
  let C be FormalContext;
  let CP be quasi-empty ConceptStr over C;
  assume CP is FormalConcept of C;
  then reconsider CP as FormalConcept of C;
A1: (AttributeDerivation(C)).(the Intent of CP) = the Extent of CP by Def9;
A2: (ObjectDerivation(C)).(the Extent of CP) = the Intent of CP by Def9;
  now
    per cases by Def8;
    case
      the Intent of CP is empty;
      then the Extent of CP = the carrier of C by A1,Th18;
      hence CP is universal;
    end;
    case
      the Extent of CP is empty;
      then the Intent of CP = the carrier' of C by A2,Th17;
      hence CP is co-universal;
    end;
  end;
  hence thesis;
end;
