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_prog_cons (r:rule) rl: (* => Syntax.v ? *) max_arity_prog (r::rl) = max (max_arity_rule r) (max_arity_prog rl).