theorem
  for X be RealLinearSpace
  holds
      the carrier of X = the carrier of (RLSp2RVSp X)
    & the ZeroF of X = the ZeroF of (RLSp2RVSp X)
    & the addF of X = the addF of (RLSp2RVSp X)
    & the Mult of X = the lmult of (RLSp2RVSp X);
