unfold UE. unfold Ele. simpl.
intros.
intro.
apply lt_irrefl with b.
apply le_lt_trans with e.
destruct (IndexSeq_inv H e H0)...
rewrite Ecmp_sym in H1.
case_eq (Ecmp T (subscript e) (subscript b)); intro; rewrite H2 in H1.
discriminate.
apply (IndicesCorrect e b H2).
discriminate.
Qed.

(* Specifications: *)
Lemma IndexSeq_cons (b: Index) l: IndexSeq (S b) l -> IndexSeq b (b :: l).
Proof with auto.