tros. omega.
- apply neq_lt_gt_iff. left. omega.
Qed.

(*****************************************************************************)
(*                                                                           *)
(*                     Translation respects PPO                              *)
(*

(* Specifications: *)
(* Translation produced an ordered TRS *) Theorem BC_to_TRS_PPO bc st n s: let trs := snd (BC_to_TRS bc st) in