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

theorem Th38:
  for e1,e2 being FinSequence of REAL for f1,f2 being FinSequence
  of F_Real st len e1 = len e2 & e1 = f1 & e2 = f2 holds e1 "*" e2 = f1 "*" f2
proof
  let e1,e2 be FinSequence of REAL;
  let f1,f2 be FinSequence of F_Real;
  assume len e1 = len e2 & e1 = f1 & e2 = f2;
  hence e1 "*" e2 = Sum mlt(f1,f2) by Th35,Th36
    .= f1 "*" f2 by FVSUM_1:def 9;
end;
