(* map a n-ary string to a binary string *)
Definition bin (x: list nat) : list bool :=
flat_map (fun (a : nat) => true :: (repeat false a) ++ [true])  x.
Definition bin_map A := map (fun '(x, y) => (bin x, bin y)) A.

Lemma tau2_bin_map {A : list (list nat * list nat)} : tau2 (bin_map A) = bin (tau2 A).