reserve X,Y,Z for non trivial RealBanachSpace;

theorem LM300:
  for X,Y be RealNormSpace,
      u,v be Point of R_NormSpace_of_BoundedLinearOperators(X,Y)
  holds u - (u+v) = -v
  proof
    let X,Y be RealNormSpace,
        u,v be Point of R_NormSpace_of_BoundedLinearOperators(X,Y);
    thus u - (u+v) = (u-u) -v by RLVECT_1:27
    .= 0.R_NormSpace_of_BoundedLinearOperators(X,Y) -v by RLVECT_1:15
    .= -v by RLVECT_1:14;
  end;
