intros.
unfold modify_seq, nat_rect in |- *.
auto with algebra.
Qed.
Hint Resolve modify_hd_tl: algebra.

Lemma modify_tl_hd :
forall (A : Setoid) (n : Nat) (v : seq (S n) A) (m : Nat)
(H : S m < S n) (a : A),
head (modify_seq v (Build_finiteT H) a) =' head v in _.