
theorem Th12:
  for X being non empty set,
      f being Function of X,COMPLEX st f|X is bounded holds
                             modetrans(f,X) = f
proof
  let X be non empty set,
      f be Function of X,COMPLEX;
  assume f|X is bounded; then
  f in ComplexBoundedFunctions X;
  hence thesis by Def7;
end;
