Proposition BC_to_TRS_rules_vars_defined bc n s st:
  let trs := snd (BC_to_TRS bc st) in
  arities bc = ok_arities n s →
  Forall rule_vars_defined trs.(rules).

Lemma max_arity_fapply_args f h n s: max_arity_term (fapply h (mk_args_h (S n) s (mk_call (S (n + s)) f))) = n+s+2.