
theorem Th36:
  for X, Y, Z be RealNormSpace
  for f,h be Point of R_NormSpace_of_BoundedBilinearOperators(X,Y,Z)
  for a be Real
  holds
    h = a*f
  iff
    for x be VECTOR of X,y be VECTOR of Y
    holds h.(x,y) = a * f.(x,y)
  proof
    let X,Y,Z be RealNormSpace;
    let f,h be Point of R_NormSpace_of_BoundedBilinearOperators(X,Y,Z);
    let a be Real;
    reconsider f1=f
      as VECTOR of R_VectorSpace_of_BoundedBilinearOperators(X,Y,Z);
    reconsider h1=h
      as VECTOR of R_VectorSpace_of_BoundedBilinearOperators(X,Y,Z);
    h = a*f iff h1 = a*f1;
    hence thesis by Th25;
  end;
