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 is the only function with maximum rank *) Lemma BC_to_TRS_main_has_unique_max_rank bc n s: arities bc = ok_arities n s → ∀ st f,