reserve X,Y,Z for non trivial RealBanachSpace;

theorem
  for X,Y,Z be RealNormSpace,
      u be Point of R_NormSpace_of_BoundedLinearOperators(X,Y),
      w be Point of R_NormSpace_of_BoundedLinearOperators(Y,Z)
  holds (-w)*(-u) = w*u
  proof
    let X,Y,Z be RealNormSpace,
        u be Point of R_NormSpace_of_BoundedLinearOperators(X,Y),
        w be Point of R_NormSpace_of_BoundedLinearOperators(Y,Z);
    thus (-w)*(-u) = -w*(-u) by LOPBAN1623
    .=-(-w*u) by LOPBAN1623
    .= w*u by RLVECT_1:17;
  end;
