theorem
  (f1|X is bounded_above & f2|Y is constant implies (f1+f2)|(X /\ Y) is
  bounded_above) & (f1|X is bounded_below & f2|Y is constant implies (f1+f2)|(X
/\ Y) is bounded_below) & (f1|X is bounded & f2|Y is constant implies (f1+f2)|(
  X /\ Y) is bounded) by Th83;
