
theorem FIF:
  for f be non empty complex-valued FinSequence holds
    Product f = f.1 * Product (f/^1)
  proof
    let f be non empty complex-valued FinSequence;
    reconsider f as FinSequence of COMPLEX by RVSUM_1:146;
    reconsider g = (f|1) as 1-element FinSequence of COMPLEX;
    A1: <*g.1*> = g;
    Product f = Product ((f|1)^(f/^1))
    .= (f.1) * Product (f/^1) by A1,RVSUM_2:43;
    hence thesis;
  end;
