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;
