
theorem
  for n be Nat,
      X be RealNormSpace-Sequence
    st X = n |-> RNS_Real
  holds product X is finite-dimensional
      & dim(product X) = n
  proof
    let n be Nat,
        X be RealNormSpace-Sequence;
    assume X = n |-> RNS_Real;
    then product X = REAL-NS n by Th13;
    hence thesis by REAL_NS2:62;
  end;
