
theorem Th31:
  for X being RealNormSpace-Sequence,
      Y be RealNormSpace holds
  (the carrier of product X) --> 0.Y
  = 0.R_NormSpace_of_BoundedMultilinearOperators(X,Y)
  proof
    let X be RealNormSpace-Sequence,
        Y be RealNormSpace;
    ((the carrier of product X) --> 0.Y)
     = 0.R_VectorSpace_of_BoundedMultilinearOperators(X,Y) by Th26
    .= 0.R_NormSpace_of_BoundedMultilinearOperators(X,Y);
    hence thesis;
  end;
