induction n.
intros.
simpl in |- *.
auto.
intros.
simpl in |- *.
red in |- *.
simpl in |- *.
intro.
elim x.
intros.
apply Ap_comp; auto with algebra.
Qed.
Hint Resolve Seqtl_comp: algebra.
(** - "hdtl" is a 'tool' for writing a sequence as the cons of its head and its tail %\label{hdtl}% *)
Definition hdtl (v : seq (S n) A) := head v;; Seqtl v:seq (S n) A.

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