intros.
apply
seq_equal_trans
with
(pred (S n))
(cast_seq (head v;; omit (Seqtl v) (Build_finiteT H)) Heq);
auto with algebra.
apply Map_eq_seq_equal; auto with algebra.
Qed.
Hint Resolve omit_tlelt'': algebra.

(* Specifications: *)
Lemma omit_concat_first_part :
forall (n m : Nat) (A : Setoid) (v : seq (S n) A)
(w : seq m A) (i : Nat) (Hi : i < S n) (Hi' : i < S n + m),
omit (v ++ w) (Build_finiteT Hi') =' omit v (Build_finiteT Hi) ++ w in _.