reserve M for non empty set;
reserve V for ComplexNormSpace;
reserve f,f1,f2,f3 for PartFunc of M,V;
reserve z,z1,z2 for Complex;
reserve X,Y for set;

theorem
  f1 is_bounded_on X & f2 is_bounded_on Y implies f1-f2 is_bounded_on X /\ Y
proof
  assume that
A1: f1 is_bounded_on X and
A2: f2 is_bounded_on Y;
  -f2 is_bounded_on Y by A2,Th45;
  then f1+-f2 is_bounded_on (X /\ Y) by A1,Th46;
  hence thesis by Th25;
end;
