
theorem Th35:
  for X being RealNormSpace-Sequence,
      Y be RealNormSpace
  for f,g,h be Point of
  R_NormSpace_of_BoundedMultilinearOperators(X,Y)
  holds h = f+g iff for x be VECTOR of product X holds h.x = f.x + g.x
  proof
    let X be RealNormSpace-Sequence,
        Y be RealNormSpace;
    let f,g,h be Point of R_NormSpace_of_BoundedMultilinearOperators(X,Y);
    reconsider f1=f, g1=g, h1=h as VECTOR of
      R_VectorSpace_of_BoundedMultilinearOperators(X,Y);
    h = f+g iff h1 = f1+g1;
    hence thesis by Th24;
  end;
