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;
