intros.
simpl in |- *.
apply Ap_comp; auto with algebra.
Qed.
Hint Resolve cons_later_elements: algebra.
(* Taking the "tl" of a sequence *)
(** %\label{Seqtl}% *)
Definition Seqtl : forall n : Nat, seq n A -> seq (pred n) A.
clear n.
intro n.
case n.
intro f.
exact f.
intros m f.
apply
(Build_Map
(Ap:=fun i' : fin m =>
match i' with
| Build_finiteT i Hi => f (Build_finiteT (lt_n_S _ _ (Hi:i < m)))
end)).
red in |- *.
intros x y.
case x.
case y.
simpl in |- *.
intros.
apply Ap_comp; auto with algebra.
Defined.

(* Specifications: *)
Lemma Seqtl_comp :
forall v v' : seq n A, v =' v' in _ -> Seqtl v =' Seqtl v' in _.