reserve X,Y,Z for non trivial RealBanachSpace;

theorem
  for X be non trivial RealBanachSpace,
      v1,v2 be Point of R_NormSpace_of_BoundedLinearOperators(X,X),
      w1,w2 be Point of R_Normed_Algebra_of_BoundedLinearOperators X,
          a be Real
  st v1 = w1 & v2 = w2
  holds v1 + v2 = w1 + w2
      & a * v1 = a * w1;
