Variant last_spec : seq T -> Type :=
  | LastNil        : last_spec [::]
  | LastRcons s x  : last_spec (rcons s x).Variant last_spec : seq T -> Type :=
  | LastNil        : last_spec [::]
  | LastRcons s x  : last_spec (rcons s x).Variant last_spec : seq T -> Type :=
  | LastNil        : last_spec [::]
  | LastRcons s x  : last_spec (rcons s x).

Lemma last_nth x s : last x s = nth (x :: s) (size s).