reserve D for non empty set,
  i,j,k for Nat,
  n,m for Nat,
  r for Real,
  e for real-valued FinSequence;

theorem
  for i for e1,e2 being Element of i-tuples_on REAL for f1,f2 being
Element of i-tuples_on the carrier of F_Real st e1 = f1 & e2 = f2 holds e1 "*"
  e2 = f1 "*" f2
proof
  let i;
  let e1,e2 be Element of i-tuples_on REAL;
  let f1,f2 be Element of i-tuples_on the carrier of F_Real;
  assume e1 = f1 & e2 = f2;
  hence e1 "*" e2 = Sum mlt(f1,f2) by Th34,Th36
    .= f1 "*" f2 by FVSUM_1:def 9;
end;
