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 F be set
  holds
  F is Subset of REAL-NS n
    iff
  F is Subset of n-VectSp_over F_Real by Th5;
