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 Post_CFG_2 x :
rewt G [S] x ->
exists A m, A <<= R /\ sigma m A = x /\ (m = S \/ m = a /\ A <> []).