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_app (prg1 prg2: list rule): (* => Syntax.v ? *) max_arity_prog (prg1++prg2) = max (max_arity_prog prg1) (max_arity_prog prg2).