case i.
intro x.
case x.
intros l j.
case j.
intro x0.
case x0.
simpl in |- *.
auto.
intros.
inversion in_range_prf0.
inversion H0.
intros.
inversion in_range_prf0.
inversion H0.
Qed.
Hint Resolve fin_S_O_unique: algebra.
(** - A sequence is just a setoid function from (fin n) to A: %\label{seq}% *)
Definition seq (n : Nat) (A : Setoid) := MAP (fin n) A.

(* Somehow this is necessary: *)
Lemma toSeq :
forall (A : Setoid) (n : Nat) (v v' : Map (fin n) A),
v =' v' in seq _ _ -> v =' v' in MAP _ _.