intros.
simpl in |- *.
red in |- *.
intro i'.
elim i'.
intro i.
simpl in |- *.
case i.
auto.
intros.
apply Ap_comp; auto with algebra.
Qed.
Hint Resolve cons_comp: algebra.

(* Specifications: *)
Lemma cons_first_element :
forall (v : seq n A) (H : 0 < S n), (a;; v) (Build_finiteT H) =' a in _.