
theorem NLM2:
  for c be non empty positive-yielding XFinSequence of REAL,
  a be Real
  st 0 < a
  holds a (#) c is non empty positive-yielding XFinSequence of REAL
  proof
    let c be non empty positive-yielding XFinSequence of REAL,
    a be Real;
    assume AS: 0 < a;
    P2: dom (a (#) c) = dom c by VALUED_1:def 5;
    for r being Real st r in rng (a (#) c) holds 0 < r by PARTFUN3:def 1,AS;
    then
    a (#) c is positive-yielding;
    hence thesis by P2;
  end;
