destruct n.
simpl in |- *.
red in |- *; auto with algebra.
destruct n.
intros; (apply Trans with (empty_seq M); auto with algebra).
auto with algebra.
Qed.
Hint Resolve omit_head_is_seqtl: algebra.

Lemma omit_tlelt :
forall (n : Nat) (A : Setoid) (v : seq (S (S n)) A)
(m : Nat) (HS : S m < S (S n)) (H : m < S n),
omit v (Build_finiteT HS) =' head v;; omit (Seqtl v) (Build_finiteT H) in _.