reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

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);
