Proposition BC_to_TRS_arity bc n s st:
  let trs := snd (BC_to_TRS bc st) in
  arities bc = ok_arities n s →
  max_arity_prog trs.(rules) ≤ trs.(maxar).

(* main always has the highest rank *) Lemma BC_to_TRS_main_has_maxrank bc st n s: let trs := snd (BC_to_TRS bc st) in