
theorem Th28:
  for C being FormalContext for CP1,CP2 being FormalConcept of C
  holds CP1 is-SubConcept-of CP2 iff the Intent of CP2 c= the Intent of CP1
proof
  let C be FormalContext;
  let CP1,CP2 be FormalConcept of C;
A1: now
    assume the Intent of CP2 c= the Intent of CP1;
    then
A2: (AttributeDerivation(C)).(the Intent of CP1) c= (AttributeDerivation(C
    )).(the Intent of CP2) by Th4;
    (AttributeDerivation(C)).(the Intent of CP1) = the Extent of CP1 & (
    AttributeDerivation(C)).(the Intent of CP2) = the Extent of CP2 by Def9;
    hence CP1 is-SubConcept-of CP2 by A2;
  end;
  now
    assume CP1 is-SubConcept-of CP2;
    then
A3: the Extent of CP1 c= the Extent of CP2;
    (ObjectDerivation(C)).(the Extent of CP2) = the Intent of CP2 & (
    ObjectDerivation(C)).(the Extent of CP1) = the Intent of CP1 by Def9;
    hence the Intent of CP2 c= the Intent of CP1 by A3,Th3;
  end;
  hence thesis by A1;
end;
