reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th68:
  for C,D being Category holds
  Funct(C,D) c= bool [:(the carrier' of C),(the carrier' of D):]
  proof
    let C,D be Category;
    now
      let x be object;
      assume x in Funct(C,D);
      then reconsider x9 = x as Function of (the carrier' of C),
        (the carrier' of D) by CAT_2:def 2;
      x9 c= [:(the carrier' of C), (the carrier' of D):];
      hence x in bool [:(the carrier' of C), (the carrier' of D):];
    end;
    hence thesis;
  end;
