
theorem Th36:
  for X being RealNormSpace-Sequence,
      Y be RealNormSpace
  for f,h be Point of R_NormSpace_of_BoundedMultilinearOperators(X,Y)
  for a be Real
  holds h = a * f iff for x be VECTOR of product X holds h.x = a * f.x
  proof
    let X be RealNormSpace-Sequence,
        Y be RealNormSpace;
    let f,h be Point of R_NormSpace_of_BoundedMultilinearOperators(X,Y);
    let a be Real;
    reconsider f1 = f, h1 = h as VECTOR
      of R_VectorSpace_of_BoundedMultilinearOperators(X,Y);
    h = a * f iff h1 = a * f1;
    hence thesis by Th25;
  end;
