End Post_CFG.
Definition Post_G '(R, a, x) := exists A, A <<= R /\ A <> [] /\ sigma a A = x.
Definition CFG '(G, x) := L G x.

(* Specifications: *)
Lemma reduce_grammars :
Post_G ⪯ CFG.
Lemma reduce_CFP :
CFP ⪯ CFP'.
Lemma reduce_CFI :
CFI ⪯ CFI'.