reserve B,C,D for Category;

theorem Th30:
  for S being Contravariant_Functor of C,D, f being Morphism of C
  holds (Obj S).(dom f) = cod (S.f) & (Obj S).(cod f) = dom (S.f)
proof
  let S be Contravariant_Functor of C,D, f be Morphism of C;
  S.(id dom f) = id cod (S.f) & S.(id cod f) = id dom (S.f) by Def9;
  hence thesis by Th28;
end;
