intros.
apply seq_equal_map_equal.
apply seq_equal_trans with (w := v ++ omit w (Build_finiteT Hi)).
apply omit_concat_second_part'; auto with algebra.
apply cast_seq_preserves_seq_equal.
Qed.

(* Specifications: *)
Lemma omit_seq_in_seq_set :
forall (n : Nat) (A : Setoid) (v : seq n A) (i : fin n) (j : fin (pred n)),
in_part (omit v i j) (seq_set v).