
theorem
  for X being RealLinearSpace-Sequence,
      Y be RealLinearSpace
  holds 0.R_VectorSpace_of_MultilinearOperators(X,Y)
    = (the carrier of product X) --> 0.Y
  proof
    let X be RealLinearSpace-Sequence,
        Y be RealLinearSpace;
    A1: 0.RealVectSpace(the carrier of product X,Y)
      = ((the carrier of product X) -->0.Y);
    R_VectorSpace_of_MultilinearOperators(X,Y)
      is Subspace of RealVectSpace(the carrier of product X,Y)
      by RSSPACE:11;
    hence thesis by A1,RLSUB_1:11;
  end;
