intros x y z.
unfold Ele.
case_eq (Ecmp e y z); intros.
apply Ecmp_eq_trans_r with y...
apply Ecmp_trans with y...
elimtype False...
Qed.

(* Specifications: *)
Lemma Ecmp_ge_gt_trans: forall x y z, Ege x y -> Ecmp e y z = Gt -> Ecmp e x z = Gt.
Proof with auto.