proposition: Lemma abb_not_in_l4: ~ In ["a"; "b"; "b"] L4.
proof: Proof. unfold L4; intros N. destruct N as (n, N). assert (R: ["a"; "b"; "b"] = (pow1 "a" 1 ++ pow1 "b" 2) % list) by reflexivity. rewrite R in *; clear R. apply pow_pow_in_inv_eq in N. - destruct N. subst. inversion H0. - intros M. inversion M. Qed.
imports: Coq.Lists.List