Hint Resolve length_concat : length construction_closed.
(* If [e1] and [e2] agree up to depth [k], then, after extending them with a common suffix [e], they agree up to depth [k + length e]. *)

(* Specifications: *)
Lemma agree_concat:
forall A (e : list A) (e1 e2 : env A) k n,
agree e1 e2 k ->
k + length e = n ->
agree (concat e1 e) (concat e2 e) n.