Lemma 2.22

If a pushdown automaton recognizes some language, then the language is context-free.

Constructive proof (p. 122)

Let P = (Q, Σ, Γ, δ, q0, {qaccept}).   The variables of G are {Ap, q | p, qQ}. The start variable is Aq0, qaccept.   Construct the rules of gramamr G as follows: