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 zip_cat s1 s2 t1 t2 : size s1 = size t1 -> zip (s1 ++ s2) (t1 ++ t2) = zip s1 t1 ++ zip s2 t2.