Fixpoint zip (s : seq S) (t : seq T) {struct t} :=
  match s, t with
  | x :: s', y :: t' => (x, y) :: zip s' t'
  | _, _ => [::]
  end.Definition unzip1 := map (@fst S T).Definition unzip2 := map (@snd S T).

Lemma nth_zip x y s t i : size s = size t -> nth (x, y) (zip s t) i = (nth x s i, nth y t i).