
theorem Th35:
  for X, Y, Z be RealNormSpace
  for f,g,h be Point of R_NormSpace_of_BoundedBilinearOperators(X,Y,Z)
  holds
    h = f+g
  iff
    for x be VECTOR of X,y be VECTOR of Y
    holds h.(x,y) = f.(x,y) + g.(x,y)
  proof
    let X, Y, Z be RealNormSpace;
    let f,g,h be Point of R_NormSpace_of_BoundedBilinearOperators(X,Y,Z);
    reconsider f1=f, g1=g, h1=h
      as VECTOR of R_VectorSpace_of_BoundedBilinearOperators(X,Y,Z);
    h=f+g iff h1=f1+g1;
    hence thesis by Th24;
  end;
