Section Post_CFG.
Variable R : stack nat.
Variable a : nat.
Definition Sigma := sym R ++ [a].
Definition S : nat := fresh Sigma.
Definition G := (S, (S,[S]) :: map (fun '(u, v) => (S, u ++ [S] ++ v)) R ++ map (fun '(u, v) => (S, u ++ [a] ++ v)) R).

Lemma reduction_full x :
(exists A, A <<= R /\ A <> [] /\ sigma a A = x) <->  L G x.