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 FinSequence of REAL-NS n,
      Fv be FinSequence of n-VectSp_over F_Real
    st Fv = F
  holds Sum F = Sum Fv
  proof
    let F be FinSequence of REAL-NS n,
       Fv be FinSequence of n-VectSp_over F_Real;
    assume
    A1: Fv = F;
    reconsider Ft = F as FinSequence of TOP-REAL n by Th4;
    Sum F = Sum Ft by Th21;
    hence thesis by A1,MATRTOP2:4;
  end;
