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 set
  for n be Nat holds
    X is Linear_Combination of REAL-NS n
      iff
    X is Linear_Combination of n-VectSp_over F_Real
  proof
    let X be set;
    let n be Nat;
    X is Linear_Combination of REAL-NS n
    iff X is Linear_Combination of TOP-REAL n by Th11;
    hence thesis by MATRTOP2:1;
  end;
