reserve X,G for RealNormSpace-Sequence,
          Y for RealNormSpace;
reserve f for MultilinearOperator of X,Y;

theorem PSPROD: ::: LOPBAN10 lemma; NAT_4:42
  for F be FinSequence of REAL
  st for i be Element of dom F holds F.i > 0
  holds Product F > 0
  proof
    let F be FinSequence of REAL;
    assume for i be Element of dom F holds F.i > 0; then
    for j be Element of NAT st j in dom F holds F.j > 0;
    hence Product F > 0 by NAT_4:42;
  end;
