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).

Qed. Lemma BC_to_TRS_rank_main_aux f bc st inf n s: let trs := snd (BC_to_TRS bc st) in arities bc = ok_arities n s