We prove here that the context-free languages family (CFL) and the matrix languages of finite index family (MLIF) are incomparable, which answers Pun's question. The proof uses properties about the MLIF already known about the CLF. In particular, we prove analogs about the MLIF of Ogden's lemma and of the Transfer theorem for iterative pairs, due to Boasson. We also give another example of the previous Transfer theorem, by proving that the full-AFL MLIF is not principal.
