intros.
simpl in |- *.
red in |- *.
intro.
apply Trans with (head v).
apply seq_S_O_contains_single_elt; auto with algebra.
apply Trans with (head v'); auto with algebra.
Qed.
Hint Resolve seq_S_O_head_fixes_everything: algebra.

(* Specifications: *)
Lemma cons_later_elements :
forall (v : seq n A) (i : Nat) (Hi : S i < S n) (Hi' : i < n),
(a;; v) (Build_finiteT Hi) =' v (Build_finiteT Hi') in _.