This paper refines the alternate stacking technique used in Greibach-Friedman's proof of the language inclusion problem L(A) ⊆ L(B), where A is a pushdown automaton (PDA) and B is a superdeterministic pushdown automaton (SPDA). In particular, we propose a product construction of a simulating PDA M, whereas the one given by the original proof encoded everything as a stack symbol. This construction avoids the need for the “liveness” condition in the alternate stacking technique, and the correctness proof becomes simpler.