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_tvl f n m: n≤m → max_arity_term (fapply f (mk_tvl n m)) = m-n.