Section MAIN.
(** %\label{seqset}% *)
Definition seq_set : forall (A : Setoid) (n : Nat) (v : seq n A), part_set A.
intros.
simpl in |- *.
apply
(Build_Predicate (Pred_fun:=fun a : A => exists i : fin n, a =' v i in _)).
red in |- *.
intros.
inversion H.
exists x0.
apply Trans with x; auto with algebra.
Defined.
Variable A : Setoid.
Variable n : Nat.

Lemma seq_set_comp :
forall v v' : seq n A, v =' v' in _ -> seq_set v =' seq_set v' in _.